I went out and picked up the Power Supply I mentioned from a place in Stortford £18 plus VAT , with a wattage of 180 instead in place of the old one's 145. I put it in without frying myself or the machine, and it's alive again. I haven't connected it up to the monitor and all, to check it's OK, but it was whirring away happily when I plugged it in, and the lights went on, so I am optimistic.

And the PCWorld repair people wanted to charge £159!

Thanks to everyone for holding my hand and making helpful suggestions. Including unnamed GUEST - and I'm normally very suspicious of them. ("Who was that masked stranger?)