Vostro 400 - computer failing to power up

This intermittant failure started 3 weeks ago, but has come and gone.

Sometimes it will start to boot, but power back down before reaching the "DELL" screen. It will periodically try to start back on its own, as it apparently still realizes that it is in the process of starting.

Sometimes it doesn't get that far.

New today, it froze on the DELL/BIOS screen a couple times, but went back to the old issue shortly afterward.

Fixes already tried, that failed:

1. New Power supply (still does it with new PSU 3 times the capability of the old one)
2. New Motherboard (acquired new MB of identical make, but Inspiron instead of Dell BIOS. Booted a couple times with new board, and had to deal with driver issues - then the old problems came back once again.  As the issue proved to not be the MB, I returned the original MB to the case, replaced everything.
3. Rechecked all connectors repeatedly, and (obviously, from the MB swap, then swap back) have reseated all the RAM and the processor itself. All are secure.
4. Removed all the USB connectors - no change.
5. Removed a PCI card that adds additional USB ports to see if it might be the issue. The card has functioned well over 2 years. It booting normally once, ran for a half hour, then shut down on me as I was typing. So, it's not the issue.

This most recent in-use shutdown  appeared almost like a button-induced hard shutdown (hitting the button to turn the machine off without shutting down Windows). IS it possible a malfunctioning power button may be the issue?