Like the title says, my computer randomly shuts off while running games. First noticed while experimenting with Aion, a few days later it also occurs with Star Wars: The Old Republic, something it hadn't done before.
The program files don't include any duplicate files (which I thought may be a problem. Aion did have a duplicate initially, and the deletion of this file appeared to fix the problem, though it returned the next day.)
Further research has indicated that the CPU maybe overheating, or the the PSU is failing. I'm not "techy" enough to know if it is the PSU, so I thought I'd ask for help.
Additionally, when the computer shuts down, there is no warning, just a black screen and then the keyboard lights and fans stop running roughly 5s afterwards.
Attached is the Speccy file of my computer's current state.