Ok, took it to the shop. The bloke there tested everything i had already tested, and concluded it was the motherboard - again. He had a new AM2 mobo in stock, so i asked him if he could fit that for me. He did (it's my third mobo if anyone's counting), and it's sort of working again.
I say 'sort of' because, after it has been left on for a certain length of time, even just idling, it'll suddenly shut down. If you try to turn it back on straight away, it'll promptly and unceremoniously shut down shortly after the BIOS screen.
Right now, i'm thinking it might be an over-heating problem. I've noticed he's put my cooler heatsink-fan on backwards. I have an Arctic Cooling Freezer64 Pro on my CPU, and he's put it on so that it is blowing hot air in towards the centre of the case, instead of out towards the exhaust fan at the back.
Does that sound like a reasonable hypothesis? Would such a seemingly minor oversight give rise to such serious effects?
This problem occurs maybe 10 minutes after turning it on, which means that the machine remains essentially unusable.
I'm not a happy bunny, but a sad panda instead.