Trying to fix my brothers friends computer

I've spent the last two days trying to narrow down the problem but it's like I've been running in circles. He bought this pc for gaming, got it second hand from a friend of mine, but he's had nothing but issues with it. The video will frequently cut out or just lock up on him, both requiring him to restart. I thought it was driver related ad a lot of the drivers were old or just not there at all, but that fixed nothing, so perhaps a hardware issue ? I installed his card in my pc and my card in his, and ran unigine to see if under load the card had issues our if it is the rest of the system that had issues, his card didn't show any of the weird cutting out like it did on his system, but when I came back in the morning my pc did notify that I recovered from an unexpected shutdown. The issue I guess that I'm having is the problem itself random at best, and as well, I get totally different results when connected to a tv I used vs a monitor I used to test. Any help in what I can do to give a solid answer on what could be causing the problem? I still post his specs and mine below

his computer:

xfx 7501 72p9 intel 775 ddr2 motherboard 

intel core 2 quad @2.33 GHz

cooler master closed loop liquid cooler for cpu (dont rember the specific model #)

xfx HD 6870 gpu

8GB (4x2) 1333 MHz Fatality RAM

seagate barracuda 250 GB HDD

thermaltake TX2 750W bronze certified psu

Have you dusted the videocard yet? i would use it in your rig for a few days and game on it to see if it does anything it shoudnt try uping the voltage a bit or lowering the clock speeds to see if it helps. Its a old videocard it might be dieing. 

+1 agree

Yeah, I took the whole thing apart, applied new thermal paste (the other stuff was rock solid and crumbling off), and ran it in my system for a day and over night, playing games and running Unigine heaven benchmark to see if it would die, but no issues whatsoever... for whatever reason it was having issues with TVs, but would run totally fine on a normal monitor, any idea why that could be ? there was a bunch of issues at first, but i fixed most of them (outdated driers, crusty thermal paste on gpu, a few other things), and now it seems to be that the case he has is choking the videocard it a very small mid atx case with no openings of fans up front, it just has the one exhaust fan, and a rinky dink little fan up top. That and it cannot seem to handle being put on a TV, and he is running this pc at home with dual tv setup, very small tvs. When run on a tv is has tearing issues and cuts in and out all the time, as well as freezes every now and then even when not running very hot on the gpu, whereas on a monitor , no tearing no flickering, and no freezing.