contrary to a couple other responses, the MOST likely culprit, and most likely from your symptoms, is a loose heatsink on your cpu. if it's come loose and isn't making full contact with your cpu you'll get exactly the symptoms you're talking about, especially the hanging during games. when the cpu heats up, as in gaming, if the heatsink has come loose it will completely freeze or crash during games.
definately check that first, take the heatsink off, make sure all the clips and ties are secure, maybe even re-apply a bit of thermal paste, and re-secure it.
give that a shot first before you start a full rebuild and pulling all your cables.