For freezing i would be looking at temps m8...why not try running rivatuner hardware monitoring on your desktop while you play a game, then when it freezes you can view the graph to see what your top temp was b4 it went tits. or if you have to do a hard reboot just collapse the desktop before it freezes and check your temps then....if ok i would be looking at your psu....350 watts just isn't enough imo.
Also can you try the g-card in another pc to see if its ok in that one?
It is just a process of elimination...i had this same problem with my sons rig...it was a dodgy mobo at the end.