Just a possibility......

I've seen this on a number of laptops by different manufacturers when they had bad batteries, or almost dead batteries with a bad AC Adapter (battery almost dead cause can't charge it with bad AC). Just enough juice to start it up partway, then it decides it doesn't have enough power and immediately shuts back down.

See if you can scrounge up a known good AC Adapter or battery for it from a friend/colleague/etc, battery probly better choice to try, and see if it boots up okay. Or if this isn't thru work, mebbe take it to a local computer store that deals with them and see if they let you test it out.

There is also the Remote chance that the voltage regulator inside the laptop is bad, but I'd check the other things first as this is less likely.

GL