Alienware m17x R3 won't power on

I have an Alienware m17x R3 that has a few issues, had some work done, and won't turn on. 

History: I got the laptop through college back in December 2011, it worked flawlessly until 2015 when it suddenly died as the final cinematic of Dragon Age: Inquisition ended (pre DLC, but hey, at least I got to finish the main story) and would not turn on again. I was unable to perform any diagnostics (it wouldn't turn on, so, you know, couldn't even get into the BIOS) so I shelved it until I could afford to send it in somewhere. The only clue given was the blue LED ring on the power cord, it would light up when I plugged the cord into the wall, but would then turn off when I plugged the cord into the laptop. Online searches led me to believe the motherboard had died based on the power cord/LED issue. The battery had also died before this and was unable to hold a charge, I was thus unable to power on the laptop without it being plugged in at any rate. There was also that time a mug of black coffee was spilled on the laptop, no sugar or cream, but that is of small comfort. When the mug was spilled the laptop shut itself off instantly, I opened it up, let it dry and air (I picked it up, tipped it, and watched a mug of coffee pour out of the *** thing), waited 48 hours and turned it on, to my delight it worked, and continued to do so for another 8 months or so. There was a fear that the acidic nature of the coffee would corrode connections and stuff, but there were no performance drops or issues that I noticed between the spill and its ultimate demise.

Fast forward to early 2017. I finally brought the laptop into NCIL in Thunder Bay and briefed them on the issues and asked them to diagnose to confirm the motherboard issue and replace it (as well as add some RAM, however in the end I chose to not upgrade my RAM). They confirmed the motherboard was toast and needed repair, and replaced it with a refurbished model. They then called me and told me the video card was also shot and needed replacing, an added cost I could not afford. When I picked up the laptop from the shop I asked if it would power on and work with a secondary monitor, they told me that without the video card (which is still in place) no display would work. 

HOWEVER: There is no change from before. The power cord LED ring turns on when I plug it into a wall, and turns off when I plug it into the laptop, still. The laptop will not power on at all. I've tried leaving the laptop plugged in for a time before attempting to power up (with and without the battery), I removed and reseated the video card and RAM sticks, no joy after any attempt. 

I'm starting to wonder if maybe they didn't actually do anything and just took my money. 

I'm reaching out hoping someone can help me diagnose what's actually wrong, or at least get the laptop functional enough to HDMI out to the TV so I can use that as a monitor. Maybe point me toward an affordable replacement video card. I'm a little cheesed that there appears to have been no improvement, despite me being a few hundred bucks in the hole. 

I don't really remember the exact specs and parts list, but I still have the service tag, so if you're able and willing to help out I can provide that so you can see exactly what parts we're dealing with. (I might need some help figuring out what motherboard was installed, if it at all). 

Thanks in advance,

Josh (VirulentGunk)