I have traced this problem to the power supply. The existing one still works partly. There is a yellow LED on the motherboard that illuminates, and I tried the trick of unplugging the 24-pin connector and connecting the pin with the green cable to a pin with a black cable, which simulates "power on". The fans immediately started at full speed, and blew dust everywhere. But I guess that one or more of the low-voltage lines no longer works.when I woke up this morning my HTPC was completely dead.
I happened to have a new power supply that I was intending to use for another project, so I have connected it temporarily, and the HTPC powers-up without problem. Unfortunately, I had removed the hard disks to copy some of the files elsewhere, and my capture disk seems to have developed the "click of death".
I looked on Ebay for replacement power supplies for the Dell XPS 420. There were several available from Germany for a very reasonable £300 each , plus one available from France for a more reasonable £66. But these are pre-loved units, and the power supply is one component that I think has a limited lifetime, so I will probably buy a new unit. The Dell power supply is near-enough compatible with standard ATX units for a standard one to fit.
-- from CyberSimian in the UK