BSOD/freezes a few times, then it works fine for a few hours

Hello there. :)
I'm looking for help. I've had some problems with my PC this month and I can't really make it work properly. It freezes/crashes/has a BSOD randomly, mostly a few minutes after it starts. It seems like it isn't caused by overheating since these errors appear independently of stress (one day I can play games for a few hours without a problem and the other day it crashes while browsing Internet).
At first, there were mostly BSODs and stuff, but it looked like it couldn’t save the memory dumps – there were no dumps seen in bluescreen viewer. Sometimes it just froze with the screen blurred and I had to restart it. After some of the crashes ‘cmos checksum bad error’ appeared while booting.
I reinstalled Windows and it seemed to be okay, but then there was a BSOD again. This is the only BSOD I can see in the bluescreen viewer. After the BSOD the bios clock was reset and I had to set it manually. I decided to clean the PC thoroughly, I even dismounted the graphical card to do it. After that, it looked like the problem was gone, but today it has crashed again. The screen went black and I couldn’t even turn it off using the power button. I had to switch it on a few times for it to run properly (before that there were only black screens and slow fans movement). When it finally turned on, there was 'cmos checksum bad error' again and it sounded weird. It was too quiet as if fans were running too slowly.
Finally, I waited a few hours and now it works ok, but I know it will happen again.
Any ideas what might be causing it? Is it a motherboard failure?
I use TrueCrypt to encrypt my HDD, but I don't think it's important in this matter, is it?
My computer specification can be seen on my profile.
Thank you in advance for your attention.