Computer help forum: Computer stuck at black screen when turning on. n

Gateway GT4022 tower
2.4 ghz AMD Anthion 64 processor 4000+
Stickers indicate Windows XP
nVIDIA Geforce 6100 intergrated into motherboard
200 GB HD
1 Gig RAM (512mb from 2 sticks) expandable to 4 Gig
2007ish machine.

I don't know the story behind it except that someone's neighbor was throwing it out and they said they could have it and then I ended up with it.

I turn it on, the fan and HD stay running, noting at all on the monitor, no cursor.
Everythign inside fine, no bad capacitors/wires.

I did this, but nothing helped:

At first, it made one short beep when turing on, now it doesn't beep.
Changed power supply.
Disconnected everything possible inside and outside then pressed the 'on' button 3 times after reconnecting everything correctly.
CPU was physically set correct. I took it out and re-installed it. Thermal paste looks good.
Tried known working RAM and tried different slots. Tried with no RAM.
Tried a known working HD.
Held down all 'f' keys while starting with a known working keyboard. A new start up for each key.
The CD drive works. It won't boot from an XP .iso CD or DBAN .iso CD.
Tried a known working pci GFX card (with a built-in fan that works on the broken machine). The monitor normally plugs into the motherboard's built-in GFX card.
Tried two known working monitors.
The light indicating that the power is on on the front of tower doesn't light up. the keyboard and mouse lights blink only right after they're plugged in.
I let it run for 15 minutes.
Removed RTC battery from motherboard for 15 mins to reset BIOS to default.
Tried with a mouse connected.
I took the motherboard out of the case and put it on cardboard and connected just the PSU and heatsink fan. There's no heatsink fan, just a fan that faces the heatsink. I tried with and without the fan. I tried with a monitor, and I tried with the HD and monitor. Nothing beeped.
Motherboard screws are not over-tighe. It was manufactured to touch the case on the underside, but there are like anti-conducting materials in those places.


How about Ultimate Boot CD?
How important is it to test the coinsized/CMOS/motherboard battery?
FWIW, I didn't use an anti-static wristband for any of this. I was in rubber sandels on carpet.


Thank you for any information.