Actually the R8 has two PCIe x16 slots per the spec below. Not knowing which slot you used, and generally it is the top most slot  closest to the CPU, it's hard to make a mistake there. Have you accessed the BIOS yet to make sure the correct GPU is being used? The following is from the support page here.

"NOTE: When a discrete video card is installed on a computer that also has an integrated video card, the integrated video card is disabled by default. Use the BIOS setup program to select which card to use."

To access the BIOS tap F12 at the Dell splash screen after you boot the system.

Table 2. Internal ports and connectors specifications .Description Values

I went into my PC's BIOS but I can't find any option to change the preferred graphics.

Can you please tell us what is the specific 2060 card you are trying to install? And you are sure you have connected the pcie power supply to the card and the GPU_PWR header in the motherboard is connected too?

i just installed a 2080 Super in my R8. System detects it automatically.

I am trying to install the MSI Gaming GeForce RTX 2060 6GB GDDR6 graphics card. It requries an 8-pin power connector and a pcie x16 slot. I have made sure to insert the card into the topmost slot (which is pcie x16) as well as plug in the 8-pin power connector. I don't know what the GPU_PWR header is, sorry.

There should be 3 power sockets on your R8 motherboard. One is a wide 24-pin ATX. Another is a 4-pin CPU_PWR. And there is one more near to the first PCIE x16 slot which is.a 8-pin socket. That’s GPU_PWR. 

1. Load pc with old gpu and monitor plugged into onboard graphics, uninstall old gpu.  Remove. (Uninstall not disable.  Don't disable onboard graphics at this point, you could once 2060 is running if you want, not necessary.)

2. Do same with new new gpu.  

3. Download and use DDU to remove any other prior gpu drivers you can find.

4. Restart and download latest gpu drivers for 2060, dch and game ready, directly from nvidia and install.

5. Restart with cable now in 2060.

Random aside but your R8 doesn't power x16 slots, you have two x8 slots (16 lanes, but only half can actually be used), if you read the motherboard you'll see it says x8.  Won't impact any of the above. Just fyi.

so it fits MSI Gaming GeForce RTX 2060 6GB GDDR6 graphics card (no URL posted by you)

9.7"long ok. (Im at MSI website now)

12 makers (yours MSI) but vast sub models made,

next is PSU power, do you have enough power (watts)?  card is 190watts, PSU they say 500w min.

YOUR CARD  has 1 , 8pin GPU-PCI AUX jack and all 8 pins must have power (and ground correct) or the car will fail.

all my 8pin GPU if you use a 6pin cable , they fail. tested by me. proof, not rumor and is makers secrets..

some manuals good tell you  this,  how to get 8 pins working, read it yet? Me to lazy.,...

what matters next are 2 things,

some dells have 8 pin cable (NOT EPS but GPU) to the PSU did you look at your PSU first, this is always first first thing, at the get go. if missing I see yours now is TWO 6 pin cables.

look for AUX power in the PC in other places, (my T3610 has PSU adaptor with that) other Dells mobo

have AUX out of the mobo,

only looking or reading the service manual allows any one to proceed.

I go to ebay and look at your MoBo, no such aux there. no PSU sold there, oops. nor cable harneses, (my lazy)

so I RTM. for you at dell.

so …. at dell manual, I see swing out PSU.  113 page long,  looking now for harness now for you.

page 47 helps, the photos are blurry, making ID hard,  but zoomed, I see TWO 6pin plugs there and no 8 pin

buy 6 to 8pin adapter. generic, GPU rated, and it will work.

IDK if dell sells adaptors for there PSU, not me,  parts list hard to find at dell.

you need at least 16amps of power on that 8 pin cable, with 3 yellow wires.(real ATX Psu have this)

PSU

~$5  6  top 8 GPU.

unless you find two 6 to one 8 pin ? really the more yellow wires connected the better it will work (less noise and more power on tap)

200watts is serious power, I have 300watt card run on my dells NO R8 here, . (all that fit that is)

the 8 pin is good 225watt total card power . Just be sure 3 yellow wires land there and all 5 grounds too.

@Aquilamaris , you previously posted that you tried to install a GTX 1080 and ran into similar problem. This was ~2weeks ago.

https://www.dell.com/community/Alienware-Desktops/Aurora-R8-GTX-1080-no-signal-from-monitor-and-keyboard/m-p/7428382#M20406

What happened to that? Did you get it to work? Or are you just tossing graphics cards out the window?

NON oem DELL CARDS will require secure boot off.

Unfortunately, I tried to install the 1080 and had no luck with it being detected by the PC during BOOT. It was second-hand, hence why I figured to obtain a brand new GPU, which is the 2060. I am frustrated to have run into the same problem with this card. 

I've checked the motherboard and all of the power sockets you listed are there and connected.

What about the "secure boot" having to be turned off in BIOS as @speedstep mentioned? Have you done that?

I disabled safe boot, used DDU to completely uninstall any previous drivers and still the RTX 2060 is not being detected by the pc! What else am I missing?

I just went into BIOS and disabled secure boot. I’ll now try and uninstall the previous drivers and reinstall the 2060.