Alright, I think I might have solved it. I finally got a chance to borrow an old PC off a friend. I was hoping to swap out the power supply however when I opened it up I realised it didn't have all the connectors I needed for my computer.
I decided to swap out the RAM just to completely rule it out and I haven't had a restart in over a day now. It still might be a bit early to say for sure, but since I bought it home from the service centre it had been restarting every few minutes.
I'm still a bit wary, since memtest never showed a single error and the restarts continued no matter which stick of RAM I used. Is it more likely I got two bad sticks that are able to pass memtest or could the memory be incompatible with my system for some other reason?