How do I go about checking to see if there's a PSU/RAM issue?
One way to check the PSU is with the Logging function of HW Info64: http://www.hwinfo.com/
The program defaults to log a plethora of otherwise unneeded information at a 2 sec interval, which is pretty long for monitoring voltages.
Go into the "Configure Sensors" menu and just pick out your voltages that you wish to monitor - especially +12 v. and +5 v. Set the monitoring interval to 250-500 ms. Start monitoring and start your game. Monitor it just long enough to see some of your problem artifacts because you will be saving a lot of data. Open the data in MS Excel, or the open office equivalent and check for wide voltage swings.