If you can get hold of a multimeter, it's reasonably easy to test a power supply. Here's a
n irritating man demonstrating tutorial on U-tube
https://www.youtube.com/watch?v=ac7YMUcMjbw
I had a very similar situation to yours a few months back and it turned out to be my motherboard that had failed even though the fans etc. were spinning up every so often.
Multimeters are cheap(ish) from somewhere like Maplins and when it's done you have a multimeter for next time.