Windows 7: BSOD playing any game, sometimes while browsing. No specific error (?)

It's been going on since I've had my PC. I had it built with all new parts from someone who I consider trusted (If I can't find a Fix here they will help me).
It happens mainly while playing games, anything from League of Legends to The Elder Scrolls: Skyrim.
It seems to happen at random intervals just more often while playing games. It says there is either a hardware or software error, I have yet to copy down everything but I don't think there was an error code.
Seeing as It's happened since I've had the computer (At first I thought it was driver problems but after updating I've realized otherwise). This eliminates the possibility of anything that I can remove physically or uninstall from the PC that may fix it (That I know of).
It didn't happen while under stress tests by who built it for me, if that's of any help.

Yeah, doesn't seem to happen when the computer is idle. However it does happen while I'm browsing the web or such as earlier when I was about to beat CLOP...
I got the stop code this time 0x00000101 Others were listed in (___) but my pc shut off before I got to record them.

I may have found the problem with a difference between the heats the cores of both the CPU and GPU were running, three on both significantly lower than the others, I have the core temp down a good 20C Seeing if it fixed my problem.

Yeah it's still doing it no matter the temp. CPU usage was at 8% and it did it....Bad RAM maybe? Though all the diagnostics I ran say everything is fine!

I got an 0x124 this time, Going to clean out my system again. Maybe this time it will help.

I've got the rest of the codes, finally did it while I wasn't too busy and the blue-screen didn't self restart my PC.
0x124 (0x0000000000000000, 0XFFFFFA800E559028, 0X00000000BE200000, 0X000000000005110A)

So. Took the PC to the shop, after every diagnostics they've done they cant figure out what the problem is for the life of them! Can anyone here respond even about looking at my stuff and seeing no problem? I feel like no ones even viewed my post though I know otherwise.

Hey joker,
If the Bsod did not display any specific error, look under the first error code in the **STOP part. Does it specify a driver or any kind of file (like a driver would be XXX.sys). If it does, go to system 32, go into the driver folder, and look for that specific file. Then, right click the file, go into properties, and go into detail (or try to just any tab) and look for the device name. try troubleshooting it or maybe disable it.

I seem to have fixed the unspecific hardware error codes by uninstalling my ASRock utilities and such, but now I'm getting a new BSOD with a 0x101 code, new files will be included.

I'm guessing now I'm going to have to reinstall windows?

If reinstalling is not a problem, I would go that route. Once we have a clean environment finding the fault should be easier.

After install, update your windows through windows update, including the drivers from windows update.

Install Microsoft Security Essentials - Free Antivirus for Windows Do not install any other software, drivers etc

Report back here if any problems, then we will continue.

Thanks

Should I re-install the current (Off the disc of course) Or do you think I could take the chance and throw a copy of ultimate on here?

Just realized in between changing rooms around, someones miss placed my CD's on me, with how everything is now it could take a long while to find.