PC black-screens shortly after launching most games

Specs CPU: i7-3770k

GPU: AMD Radeon HD 7790

Mem: 2x Corsair Vengeance DDR3 4Gb

Mobo: ASUS P8P67 LE

PSU: Kingwin MK-650W

It's crashed on the following games: The Forest, Overwatch, World of Warcraft (very shortly after launch, sometimes I can't even select a character before a black-screen and restart), and Earthlock. Earthlock can be played for a relatively longer period of time before the crash. Big Pharma doesn't appear to crash the PC at all (I played for almost an hour plus before I exited and went to sleep).

When it crashes, I'm not hearing any audio repeat and I don't get a bluescreen, it just dies as if someone took out the power and then immediately restarts.

Things I've tried:

• Updating graphics driver
• Reseating the graphics card
• Launching games in safe mode + networking. This seems to work although I'm not sure if it's because the issue with a driver or the greatly lowered performance prevents something else from tripping up.
• Installed GPU monitoring software. Didn't really notice anything I would consider anomalous behavior before a crash. GPU temp rises but I'm attributing that to launching a game,
• Went to a restore point on 12/31. Still crashed, which rules out any recent software updates.

I'm thinking that it might be a driver issue (due to everything working in safe mode) or a power supply issue (my current one is several years old and it might not have been the best quality in the first place).