S2719DGF, connecting second monitor

@CluelessChrisOk, quite a bit to address here....

First, you say you attempted daisy-chaining, but the S2719DGF doesn't offer a DisplayPort output to facilitate daisy-chaining, so I'm not sure what cabling arrangement you tried that you thought constituted a valid daisy chain.  A daisy chain only works when the entire chain uses DisplayPort, and the way it's set up is that the first display in the chain needs to have a DisplayPort output, which would be used to feed the DisplayPort input of the next display in the chain, and so on if you use more than two.

Second, as to that USB to HDMI adapter you linked, that normally isn't a great way to connect a display, because the "indirect display" technology that has to be used by USB adapters such as those in order to carry video over a regular USB connector introduces some drawbacks even when it works.  I'll get to that a bit later.  The only real times they can be useful are for exceeding the maximum number of displays that your GPU normally supports, since indirect displays don't count towards that (because the GPU isn't directly driving them) and/or when you need to connect displays that your laptop doesn't have built-in outputs to drive.  It seems like both of those issues may be factors here -- more on that below.  Those adapters also require special drivers to be installed, otherwise they don't work at all, so that might have been a problem too.  But on top of all of that, the Amazon product page you linked indicates that this particular adapter is limited to a maximum resolution of 2048x1152 -- or 1920x1080, when considering resolutions that are actually in use today -- which is well below the S2719DGF's resolution of 2560x1440.

On the subject of number of displays, are you trying to keep both your first external display and your laptop's built-in display active when trying to light up this second external display?  If so, that could be an issue too, because I believe that system only supports two simultaneous independent displays total.  So you might have to go to Windows Display Settings and set your internal display to "Disconnect this display" before you'll be able to light up an additional external display.

In terms of exactly how to connect it, photos of this system indicate that its only native video outputs are DisplayPort and VGA.  The latter is useless in this case because the S2719DGF doesn't have a VGA input, and a VGA signal can't be adapted to any other type of signal (and VGA looks pretty bad anyway, being an analog signal).  I'm not sure how you tried the DP cable that came with the display if you've already got your only DP port occupied.

In terms of solutions, you could try either of these options:

• A DisplayPort MST hub like this one, which will allow you to drive both of your S2719DGFs as simultaneous, independent displays from your laptop's single DisplayPort output.  DisplayPort uniquely supports that capability.  (The USB connector is there purely to provide power to drive the adapter.)  This is essentially a way to create a daisy chain type of setup when your displays don't have native support for daisy chaining.  Obviously the displays aren't connected to each other in this scenario, but you realize the same end result of driving multiple independent displays from a single system output.  You would however have to keep your built-in display unused when using two external displays this way.
• A USB 3.0 to HDMI adapter that actually supports your display's resolution, like this one.  There's even one that will support up to 4K 60 Hz, but it costs more.  However, unlike the MST hub above that will keep both displays directly driven by your GPU, this is an "indirect display" solution.  As such, you'd need to download and install DisplayLink software from DisplayLink.com to use it, and as to those drawbacks I mentioned earlier, I went into detail about them in the post marked as the solution in this thread.  However, the advantage is that it would allow you to keep your built-in display active for a total of three simultaneus independent displays.

@CluelessChris  in addition to all of the above, I forgot to address the high refresh rate of the S2719DGF.  It supports 2560x1440 resolution at up to 155 Hz.  If you use an MST hub, you might have to run both displays at the standard 60 Hz.  You might be able to go slightly higher than 60 Hz, but you definitely wouldn't be able to run both at 155 Hz because there simply isn't enough bandwidth from that single DisplayPort output to run two displays at that resolution and refresh rate.

And if you go with the USB 3.0 adapter option, the first display connected via DisplayPort would likely be able to use a high refresh rate since now that port's bandwidth is only driving one display, but you might find that the adapter would still limit the second display to 60 Hz.  I don't know if the DisplayLink chip in that adapter supports anything higher than that, but I may be wrong.

And come to think of it, even for the first display attached via DisplayPort, even though the bandwidth would be available to run 2560x1440 at 155 Hz, I don't know if the GPU in that system would actually support that refresh rate.

Out of curiosity, why did you choose this display model?  It's a gaming-oriented display, but your laptop isn't set up to run two of these displays they way they're supposed to be run, and its hardware wouldn't be fast enough anymore to play games at a frame rate that would take advantage of its high refresh rate anyway, in fact it might not play them at ANY playable frame rate, especially if you tried to use its native resolution.  And I don't think you'd even be able to run FreeSync either, possibly not even with a new laptop.  I don't have as much experience with FreeSync, but I know that on the NVIDIA G-Sync side of the house, most laptops even with NVIDIA GPUs can't run G-Sync, because G-Sync requires the NVIDIA GPU to have direct control of the display output, and for reasons not directly relevant to this topic and that are longer than I'm willing to get into at almost 2 AM my time, the majority of laptops wire all of their display outputs to the Intel GPU, with the NVIDIA GPU operating as a "render-only" device when needed.  But that architecture prevents the use of G-Sync.  You might find that AMD's FreeSync has a similar requirement and would therefore face a similar problem -- on top of the problem that AMD GPUs are pretty rare to have in laptops at all.  Are you also using these displays with another system?  If not, for roughly the same price as the S2719DGF you could have gotten a 27" 2560x1440 display that gave up the gaming-oriented features like high refresh rate and FreeSync in favor of things like better color gamut and accuracy, wider viewing angles, thinner bezels, DisplayPort daisy chaining support, a USB-C input that could be convenient for a future laptop since it would carry video, USB data, and power to charge the laptop over a single cable, etc.  The Dell P2720DC is a good example of that type of option.

Thank you for the reply and I appreciate all the info you put into these posts. 

Some background; This current configuration of laptop and hastily ordered monitors was a temporary solution to the sudden work from home requirement. I originally purchased 1 S2719DGF on a recommendation but wasn't informed on all the specs and requirements of my PC. However it worked with the Dual-Mode display port cable and I am happy with the result. I subsequently ordered a second S2719DGF without any thought and ran into these (avoidable) problems. I am not using the monitors for gaming per se but do need high performance.

If you can answer some follow up questions, I'd be grateful: 

1. Just so I understand this correctly, if I go with the MST displayport hub, you're saying I won't be able to use the 2 S2719DGF as independent displays but I would still be able to use both of them as an extended display? For the time being I only need them to be extended displays and not independent of each other.

2. If I go with the MST displayport hub, is there any reason to think I would not be able to use 3 or 4 S2719DGF displays? (This would be temporary for what it's worth as I understand this is not a good long term solution and I might suffer some performance degradation in the meantime). 

3. I am in the market for a new desktop PC. Not concerned with cost. As mentioned, it's not for gaming exactly but does require high performance. Can you recommend a high performance PC that is capable of supporting several monitors easily? Ideally it would support the existing S2719DGF monitors I currently have but not absolutely necessary. I am looking into Alienware and Razer desktops but some guidance on exact models or specs would be greatly appreciated. 

As the name implies, I am quite clueless on this type of stuff and appreciate all your help.

Thanks again and in advance for all the info. 

Hey @CluelessChris , glad you found my posts useful.  I'll answer your follow-up questions one at a time:

1. "Extended display" and "independent displays" are the same concept, because in an extended display setup, you're showing different content on the different physical displays, hence they are operating independently of each other.  The opposite of extended/independent displays would be duplicated/mirrored displays, which is all you can get from non-DisplayPort outputs by using splitter boxes.  As I said, DisplayPort is uniquely able to run multiple simultaneous independent displays from a single output, such as a setup of multiple displays in extended mode, and an MST hub taps into that capability.  You can certainly set them up as mirrored too if you wanted to, though.  With an MST hub, Windows will see two individual displays attached, even though they're both running through the same physical output, and that means that you can then individually configure those displays to behave the way you want, either duplicated or extended/independent.

2. You would not be able to run 3 or 4 of these displays from an MST hub -- although you must have quite a desk to even be contemplating that setup.  As I said above, the bandwidth available from a single DisplayPort output means you might only be able to run two of these at the industry standard 60 Hz refresh rate, not their 155 Hz gaming-oriented maximum.  Display signals require bandwidth, and the bandwidth requirement is determined by the resolution, refresh rate, and color space of the display.  For non-HDR displays, color space is constant.  But you can't just run an unlimited number of independent displays from that single output.  You could get a splitter to MIRROR the same image across multiple displays, but that's not useful for most people.  The additional limitation is that I'm pretty sure the Intel HD Graphics 4600 GPU in your system is limited to two simultaneous independent displays maximum, regardless of any other limitations that may be involved, which I also mentioned earlier.  I realize you also have an AMD GPU, but on most systems the discrete GPUs are not directly controlling the display outputs, so the Intel GPU's limitations would still be a factor -- and for that matter I'm not sure even Radeon laptop GPUs of that era supported more than two displays either.  If you want to run more displays than that, you'd be looking at "indirect display" adapters that I can get more into if you're really curious.

3. I can't really advise you on what new PC to buy when you just say you want "high performance".  That isn't specific enough.  What type of things are you doing on your PC?  There are workloads that are highly storage-intensive but don't require a lot of CPU, in which case you'd want a very fast SSD but a top-end CPU would be a waste of money.  There are other workloads that require a lot of CPU horsepower and sometimes memory, but aren't very storage-intensive.  And that's before even thinking about the GPU.  If cost truly is no object, then you can of course just max out everything on a system configurator and you'll have "high performance", but you'll likely have wasted a bunch of money.  But in terms of being able to run the displays you have, basically any GPU you'd get in a nice desktop PC would be able to run at least two of those displays, and possibly up to 4 of them depending on the GPU model and the ports it offers.  Even today's Intel GPUs can run 3 of those at their default 60 Hz refresh rate as long as the system has the necessary ports to connect them -- although again I'm not sure about running 3 at a higher refresh rate.  Higher refresh rates tend to matter most to gamers, and even there these displays are relatively niche rather than being the norm for all gamers, so I don't have as much direct experience to draw on in order to know precisely where the limit is when using high refresh rate displays.