But I tried the same RAM with the perfectly functioning PSU on this computer as well as the one on there currently.
Thing is the RAM isn't under load when I'm running Prime, the CPU is. Is there a chance the PSU hurt everything? Should I do a full on swap of my parts except the CPU?
What speed and timings is your ram at? Auto can be a bit funny but set it to 1600 8-9-8-24-33-1t manually and see if it persists. Also auto ram volts is 1.54 so go to the overvolt menu and set memory to +110mv.
I would also get out the multimeter and see how much your rails are dipping under load..