I went back to troubleshooting my expensive box of dysfunctional hardware today, but I actually couldn't test any further. The next thing to check was the power supply, but I didn't have a spare ATX unit to pop in.
Sadly, I had to bite the bullet and take the thing into a trusted PC shop. There, the bloke tried a new power supply, but it made no difference. That leaves pretty much just the CPU and motherboard to test. I bet it ends up being the sodding motherboard. That'll give me another thing to send back to the place I purchased it. What a hassle. Buying hardware on-line is fine when everything works, but when it doesn't...
Anyway, they probably won't even start to look at it until early next week, so I'll forget about it for the next few days.