>5. Another general troubleshooting tip - as a rule of thumb, 80% of hardware problems are actually caused by bad contacts. You can unplug any removable components, run some contact cleaner over the connectors and reconnect them. Dust buildup on densely packed surface mount components can cause partial or complete shorts. IOW cleanliness is next to happiness :)
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>Maybe your compressed-air cleaning effort blew some dust into places it shouldn't be. In that case you might need to do a significant teardown to expose all the electronics and make sure they're clean.

That's what I thought, but then it hit something that isn't detected until POST. And I know about the "unplug and replug everything" technique, been doing that since 1989, and it usually worked :).

In this case I think the mobo just got seriously confused with something. Since the BIOS has a bit of code which enables it to play audio CDs without even booting (truly a multimedia machine), I figured it would try to spin the disk. So during one of those "lights will be on for a little longer if I keep this button pressed" periods I managed to insert a boot disk... which it would spin, but wouldn't run. Then, two days ago, I inserted a real audio CD (the oldest one I got, Jethro Tull Thebestof, 1996 or 7), and noticed that it stayed powered on while the door was open... now that's a symptom that nothing's wrong with the power (and I kept swapping the old and new battery, that I bought just a couple of weeks ago... so maybe I accidentally kept it without power long enough for it to forget the confusion)... so I inserted the audio CD and it absolutely refused to boot from it, but instead offered to boot from disk. Voila!

Don't know what was wrong, don't know what fixed it, and I'm glad I didn't have to open it.