After considerable humming, ha'ing and dithering, I delivered my unworking PC to Stockton Computer Centre at midday. At half-past three, they called me back to let me know that they had transferred the graphics card, sound card, memory, ISDN card, floppy drive, Zip disk drive, CD-ROM drive, CD-ROM rewriter and hard drive across, reinstalled Windows 98SE and installed all the drivers for the hardware on a new motherboard with a new processor (Duron 1200) in a new case with an upgraded power supply, extra USB hubs and so forth. All for GBP 170. This was after a little reluctance to commit to being able to getting the changeover done within little over 24 hours, which counts as underpromising and overperforming.
The new machine boots up much more quickly than the old one - always handy for Windows, that - and is noticeably faster. The case is easier to put on and get off. The annoying high-pitched squealing noise present on the old machine has gone (can I hear a quieter, higher-pitched one, though?) but there is a very large fan indeed attached to the Duron which is rather loud - probably too loud to sleep through, I fear.
I haven't given the machine much of a test yet and I am sure that the machine will slow back right down once I load it up with crap applications once more but there is a definite whoo-hoo on standby for the Stockton Computer Centre. So far so good!