Ok, two things spring to mind, one is an issue with the cards (this is not my first thought of the issue, but it is the easiest to test as you have 2) take the two graphics cards out and just use one at a time to see if the problem still occurs. There is a chance one of the cards has gone wrong.
How long to you manage to play a game for currently? My friends computer had a freezing issue but in addition to freezing, as soon as he enterd a game it crashed out and it was one of his cards that was the problem. If you are able to play for a while I am guessing it is not the cards that is an issue, but as I said earlier, as you have two of them it is easy to test.
The other potential problem is the RAM. Judging by your symptoms I would guess this is the issue, but as you have so much RAM I figured testing the GPUs would be quicker - hence suggesting that first.
I would suggest you remove all your RAM. Then, insert just one module and start up the computer and try playing around. If the computer does not boot then it is safe to say the module you are using ha become faulty, if it boots but the freezes occur, it is also likely the module is faulty. Do this for each RAM module, put any that cause problems to one side and once the testing is complete, put the remaing modules back in the motherboard and play, you should find it works fine.
If RAM is the issue, make sure that the remaining RAM that works is put in a dual channel configuration (if 5 modules work only use the 4 of them and keep the other spare. As a dual channel RAM kit and motherboard work best in dual channel surprise surprise
Also, if the RAM is the issue, don't worry about buying more - 4gb is all you need for gaming, anymore than that is giving no performance boost to you. So by all means RMA the faulty modules if you can, but if you cannot, don't bother worrying about spending money on replacements if you still have 4gb working