I forgot to mention a couple of other things I tried:
I replaced the mobo battery with a new one.
And I found the CMOS reset jumper & moved it to the other position, then moved it back.
(I've searched the boards for this and found several similar posts, but none close enough for me to be sure they're the same, so I'll beg your indulgence)
A couple of weeks ago, my 3 year old home PC just quit in the middle of the day. My wife said it flashed a message - something about the floppy drive, then just went blank.
Cut to the end of the story (I'm trying to balance giving all the info & testing I've done vs. overload):
When I press the power button, the box goes on, all fans (case, power supply, & CPU) go on. The monitor does not display anything - the power light stays amber (it's on, but not receiving a signal).
The keyboard lights - all 3 of them - go on, and stay on.
There are no beeps, at all.
When the hard drive is connected, I can hear it spinning up - sounds normal.
(all of the below changes have been made both individually & together with each other)
I've tried disconnecting all peripherals, including all drives. By "disconnecting" I mean I removed the cables from the motherboard and the power cables from the drives.
I've tried replacing the power supply.
I've tried replacing the AGP Video card with a new PCI video card.
I've tried replacing the CPU (old one was a Celeron 1.7Ghz, new one is a P4 1.8Ghz).
This change actually made a small difference - before the change, when I held the power button to turn off the power, nothing happened - the power stayed on, and I had to flip the power supply's switch.
With the new CPU, holding in the power button for 5 seconds does turn the unit off.
I tried the old CPU in a new motherboard, and the new unit didn't even power on (well, it did, but very briefly).
I tried with no RAM chips in, and 1 at a time (of the original 2). And I tried them in different slots.
Is there anything else I can try?
The conclusion I have to reach is that the CPU & motherboard died at the same time - what are the odds? (that's not a rhetorical question - is there a good chance that happened?)
But I don't consider myself a hardware expert, so I'm wide open to additional thoughts and suggestions.
TIA.
PS - I'm trying not to x-post this too much, but I'm desperate for an answer, so I will probably post this on a couple of boards. Thanks for your indulgence.

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