At first I thought that the screen had just gone dead, but waiting for it to start up and then doing things that would normally make noise failed to do so, and hitting the power button and then return failed to make it shut down again. It also refused to start up off of a system CD (although it did eject it, and my CD drive has been acting up of late). Unplugging all of the peripherals had no effect.
I tried holding down command-option-p-r to reset the PRAM, but after the initial startup sound nothing happened -- there were no additional startup sounds or anything.
Finally, unplugging the battery and leaving it out for a few minutes seemed to do the job. On starting up it informed me that the system clock had been reset to (I think) 1901.
It seems to be OK now, but I am wondering how dumb it is to continue to rely on this computer, which is a few years old (I believe I bought it in 2001) and out of warranty and is the computer I use for everything (including all work stuff -- I work from home).
I was really hoping to hold off on buying a new computer for another year, too. :-( It isn't impossible for me to buy another one now, but it's an expense I would prefer to avoid.
All comments welcomed ... I hope my little mac starts up in the morning!