Based on your description of playing a game for a few hours, and then the graphics card fan goes wild, it then blue screens, I'd guess that the graphics card is overheating too.

ATI cards seem to run hotter than Nvidia in my experience, so airflow really matters, and a 6870 is pushing 5 years old at this point so unless you maintain it, the potential for dust build-up in the heatsink fins and thermal paste degradation is fairly high.

The BSOD message will probably have an IRQ_NOT_LESS_THAN_OR_EQUAL_TO, or maybe just an error in one of the ATI drivers. The first 1/3 of the BSOD message is usually quite helpful in narrowing down the culprit if you note it down.

Out of your choice of potential money thrashing, I'd recommend a fresh OS install first, then Gfx card, then SSD, and finally RAM if you really want it, although these last two are about even, and a new SSD may also mean another install if you are unlucky (I was).