Suspecting that it must be a RAM problem
While reading the title, that was my first thought. If you could possibly find another set of modules to test with, it might save you from the headache I've experienced.
I myself only have 6 days uptime since replacing RAM modules. After fighting system freezes for a long time, I replaced the graphics card and then a few weeks later the motherboard. A family member finally volunteered their machine in troubleshooting. We found the memory modules had different symptoms in a machine with dedicated graphics. My system with dedicated graphics would freeze. My relatives PC with Integrated graphics would freeze with a scrambled display.
With that said about my system freezing, I have also experienced the occasional system shutdown and reboot. In fact each time it did my system time was reset, as if I had a low BIOS battery. This is when I started to suspect my motherboard. After replacement though, the second motherboard had no effect on the issue.
I would do memory test as well as switching them out, and only running one module at a time. All test would pass and switching the modules never changed the symptoms. I finally came across someone that suggested Sandy Bridge didn't play well with 1.65V memory modules. I don't know how true it is, but I was definitely having issues with those RAM modules for some reason. I'm not sure but I think the incompatibility was making them worse. Because in the end they were unbearably freezing 2 minutes after bootup.