I would lean on the video card as a possible cause. Even though may have had good use until now, it has finally reached a point to give up. Alot is going on with the video card besides demanding a glob of power it also drives a "large video display". That scan rate and all it details becomes a huge task and on top of heat stress will find the weak link. Plus, you seemly your ad-hoc connection could also be an issue or it just adds to it all. In other words, you try to make this as clean as possible. The video card IMHO is stressed out(heat build-up) and one clue it blanks out but PC stills seems to be running. What you do after that is only going to compound into multiple problems, when the real issue is video alone. The simplest test is to swap out monitors or cards or both(test alone, separate) and do this on a long time frame. Alas, because you've had similar results with yet another PC also the problems arises after some time. What may seem like a simple task, is really a day in, day out hard one for the PC to maintain at whatever levels. Even if it falls within specs and can deliver it can't over the long haul, that's proven because this has happened on 2-PCs.

Fix: replace PSU with better wattage and another good known video card/source.

IMHO, your TV monitor maybe overall the crux of this situation. Check 100% the specs and clean-up connections. I find concoctions of sorts always tend to be hard to resolve because you have so much to wade through.

tada -----Willy Happy