Computer stays on, but computer locks up

This is for my sister's computer and she keeps telling me the computer crashes. Recently she had a similar issue where the computer screen would go black after weird artifact flashing and whatnot so I thought it was driver related, or GPU related. I swapped her old card for a new 285 GTX, but it's still doing it. Testing out several drivers as well as programs to test if the GPU is faulty it gives no clear sign that it's the GPU. I tested out the CPU as well, and the RAM sticks but to avail they're all healthy fully function parts.

I did a complete OS reinstall for her to rule out if it's any software related issues, but yet again the computer crashes. It doesn't give any errors when turning back on and acts like normal and this happens at random times, sometimes in an hour, or in a couple days. Lately it's been getting worse, and I've come to suspect it might be her motherboard, but that's just my guess after ruling out the other hardware related things.

EDIT: Oh and I got her a power supply too, so it can't be it.

Anybody know what's up?