Just to close this thread off, I updated it on January 14th, and the bottom line was that nothing I tried brought it back to life. I toyed with the idea of replacing the motherboard, but that meant buying a new processor and new RAM, which I decided wasn't worth the cost for a hardly used backed machine.
So, I stumbled across a desktop on Facebook marketplace. For €45 I got a Fujitsu Celsius W370 E80+, with a decent 2.83GHz processor, 4GB RAM, and 500GB HDD plus a decent mid range graphics card. It was running Windows 7 Pro 64-bit, so I've done a clean install of Windows 10. It's quieter and faster than the old machine, so I'm well chuffed.
Thanks for the help folks.
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