Took the computer apart today to first see if I could get it working, and secondly to see if I could salvage any parts if I couldn't get it working.
Did some PSU tests with a multimeter (I had assistance from my Grandad - he has Electrical qualifications so was able to assist me), but there was 0V on all the outputs that I could test. Zilch.
So, with his assistance and knowledge, and a very careful hand, we disassembled the PSU completely. Before you say "THIS IS DANGEROUS AND STUPID!!", I know, I am fully aware of the dangers. But I had my Grandad's assistance, and was very, very careful.
Anyway, disassembly of the PSU found lots more dust, and a burnt out voltage regulator. Taking the PCB out of the housing showed the burnt out voltage regulator had actually burnt the underside of the PCB, and the laminate of the board was peeling away. So even if I installed a new regulator, the board was broken. I wasn't about to buy a new PSU off ebay, so decided to scrap the PC.
Was actually quite interesting, I don't do very much hardware stuff, so this was a good look and insight. I salvaged a GPU, some RAM, a DVD Drive and a few assorted cables. Didn't salvage the CPU, although I was tempted, I have no use for it and it was only a low end CPU anyway. So I didn't see the need. It was filthy too!
Anyone else find smashing a HDD up really satisfying? After salvaging a few magnets from the inside (they're really strong), I took a hammer to the platters. If anyone managed to get the data off them now, they deserve a prize!
So, I do believe, judging by the amount of hidden dust under and inside components (especially the PSU), the computer had overheated, and the heat burnt out the voltage regulator in the PSU. Hence the BSODs before when they used the DVD drive, the PSU couldn't cope with the extra power draw.
The lesson once again is, clean your PC regularly, or at least use it in a fairly dust free environment!