Computer won't boot

I have an older computer with a Gigabyte GA-P35-DS3L motherboard that
I home-built a few years back. I recently built a new computer and
have been keeping the old one alive until I get the new one all
checked out and settled in.

Yesterday the old computer wouldn't boot. It makes a BEEP about one
second long during the boot process but won't go any farther. The
drive lights flash and the monitor goes through its first sign of
lighting up, after I turn the computer on, but this is as far as it
goes. The monitor goes black and the activity lights on the front of
the computer flash a few times, then everything stops.

I've tried using the original Windows XP Pro installation disk, and
also a second boot disk that I slipstreamed with SP3 on it. Neither
boot disk will initiate a start-up process. The CD drive light flashes
a few times then quits and nothing more happens after the BEEP.

Any ideas as to what I might try next?

Thanks, Gordon