M17x-R3, Nvidia 580M, Intermittent Problem (Crashes, 8-beep)

I hope someone here will have suggestions on how to fix this problem.  

I have an M17x R3 with 580M and a premium LCD screen for 3D. The warrantee ran out about a year ago and just before then, the LCD screen was replaced along with some repairs to the frame. At that time all the drivers on the system were also checked and any needed updates made.  Since then the only driver I have updated is the video.

From that point, the computer ran flawlessly until 11/11/2013. It then had a single crash then worked normally for several days. Since then the crashes have become more and more frequent. Initially I thought they might be heat related and it is possible the computer overheated at some point, although I had used compressed air to blow out the vents I did not open it until the crashes became more frequent and the heatsinks had accumulated lint.

My initial diagnosis based on the lint was a heat-related video card failure. I cleaned out the lint with the hope that maybe nothing was damaged and it would work ok once the overheating was eliminated.

However, the computer continues to run off and on, sometime experiencing periods where it will run fine for a full day, other days crashing within minutes everytime I try to boot it up or even going to the 8-beep error code.  It seems to crash faster when there is a heavier load on the system (crashes sooner if attempting to play Skyrim than it does idle or browsing).

Hardware testing during longer stable periods has come back with everything checking out fine. Running a GPU status logger records no temperatures much over 60C while online sources suggest it should run to 77C before the overheating limiter kicks in. No significant changes in the GPU status (temp, clock speeds, memory usage) occurred before crashes. Given how far below the limit this is, I'm not sure the amount of lint I cleared out would have caused it to get to the point of causing heat related damage.

Most of the time it runs stable in safe mode -- I have yet to experience a crash while running in safe mode, but have not left it running in that mode for as long a period of time.

I have been using NVidia's GeForce experience to stay on the latest drivers.  I noticed there was a new driver around the time the crashes started so tried doing a roll-back. For a couple hours I thought that had worked then the crashes started again. It was at this point I first experienced the 8-beep code.

An 8-beep error code is indicated to be an LCD failure. I'm not sure how an LCD failure would cause the entire system to shut down rather than the screen just going blank. I'm also not sure whether it might simply be a loose connection on the LCD since it seems intermittent.

Anyone have suggestions on what to try at this point? If it's the video card I'll replace it, but I'd hate to replace the video card then need to replace the LCD or vice versa, or replace them and still not be able to fix the problem, or replace them and find out it's fixable without a major hardware purchase.