I have worked with pc's for 20+ years - I bet you have an issue with your PC - either the RAM is bad, or there is a mismatch between the motherboard and RAM. I've seen it many times.
You only see problems when using programs that stress the RAM/cpu, such as bitcoin-qt does
Do a memory diagnostic - Windows 7 and 8 have a built in one. Let it run overnight. If it passes, pick the advanced test and let that run overnight again.
Do not use your wallet on that PC until you are 100% sure there are no issues. Else you could courrupt it.
If it is not the ram, it could be the hard drive or sata cable connecting the drive. But that's less likely then a RAM issue
Good luck