Go back to a single DIMM in the original socket (nearest the CPU).  Verify that there are no bent pins in the sockets. Then check and reseat ALL of your power connections.

Hope this is a minor issue as it sounds (seating).

Thanks for the suggestion -- I'll try it out. I did try to upgrade my RAM to 512 MB (2 256 MB modules) from 384 MB (128, 256 modules). After that it wouldn't boot up at all -- I then reverted to my old configuration which was working so far, and still the same issue.

Try unplugging the power cord from the back of the tower and UPS.  Then replug it to the tower and a known-good wall outlet.

Any electrical events lately?  Has the system been physically moved?  Any hardware added ?

I tried all of the above suggestions, but still no resolution. I even removed both of the DIMMs and tried to boot it, expecting some kind of error beep, but it still displays the exact same behavior. Any more ideas on what could be wrong and/or how do I proceed from here?

Thanks.

At this point I'd try removing the heatsink and reseating the CPU.

If at that point you still have no beeps or diag LEDs on back, you've likely got a damaged MB or a lesser chance of a bad CPU.

If you want to narrow that down, take the CPU in an ESD bag to a local vendor (after calling), and have them test it in a PIII machine.

The CPU would likely be cheaper to replace than the mb.

Good luck, I'm still hoping it's something overlooked.  It sounds as if something went wrong during the RAM upgrade.