I've been having this problem since last Saturday and I've been trying to sort out this problem and it's really starting to drive me crazy.
I had spent £400 on computer parts had an IT tech install them all, and he made sure everything was installed correctly and it seemed like we were ready to go.
But I've ran into the same problem that my old PC used to do, the PC would just freeze at random, sometimes it would crash in 2 hours or it could take up to 2 days or an entire week.
This new built PC however seems to crash A LOT more then my other one, the longest the PC lasted without crashing was probably around 30-45 minutes. There are no blue screens when the crashes happen.
I used some old parts for this new build, believed that it wouldn't be needed to be upgraded, I had kept my GTX560ti, 650wat Corsair PSU, two harddrives (One an 500gb Hatachi and the other an 1TB Samsung which I found out was broken.)
My build is -
Intel i5 - 3750k @ 3.4ghz, I turned off it's turbo acceleration.
Gigabyte Z77-D3H Intel Z77
Corsair Vengeance Low Profile 8GB DDR3,
And the old parts that were installed are-
MSI GTX560ti Twin Frozr
LG DvD Drive
Corsair Enthusiast Series TX650
500gb Hatachi Sata Drive (I don't use the 1TB hard drive no more because of it being broken.)
I did a memtest on the RAM to see if that was the problem, it crashed. So I took out my graphics card, ran the memtest again with the 8gb installed, but it crashed again. I took out one stick of RAM and ran the test again and then it passed the memtest, I then took out the stick that passed the memtest then installed the other one, it passed the memtest again, out of the sake of curiousity I installed the graphics card back into the motherboard with both of the sticks of RAM installed as well and ran the memtest again, it passed the test with both of the sticks of RAM installed.
I was told to send back the RAM anyway, seeing how it was the easiest part to replace and is mostly the problem at times and I've gathered that I doubt it was the RAM and graphics card that were causing the crashes, the only thing I could imagine that is causing the crashes is the power supply due to how there's no blue screen errors whatsoever.
I need some help here cuz I'm really left scratching my head and I'm frustrated with this, as you can probably imagine.
The parts aren't overclocked as I don't want to do so yet.
I had a problem similar to yours, and I was dumbfounded for 2 years, I could run just fine in applications but as soon as I started a game I had 20-30 min before it just shut down, no BSOD. I tried everything, cutting back on the RAM, cutting back on HDDs and optical drives, but nothing worked. I had no onboard video so I borrowed a graphics card and it worked fine with that card so I bought a lower power card, that helped but it still happened. Finally I borrowed a power supply, it worked, no hitches, so I bought it. Funny thing was, my original power supply was a 1000W from a good brand, and this one was 430W also from a good brand.
So, back to your problem...based on my experience, I am fairly convinced that since this is a problem with your old and new computer and the PSU is one part that has remained, that is the source of your frustration. My suggestion, see if you can borrow one before you buy to confirm my suspicion, and if you do need to buy one look for one with plenty of Amps on the +12V rail, prefferably a single rail, and use NewEgg's power supply calculator to get an idea of what wattage you need (it will over estimate) then look for a power supply in that range that is rated for continuous use as these seem to be far superior in my experience. You will probably be looking at no more than $125 USD.