Did you just get to it today and it didn't boot? Did it shut off randomly? Does the LED on the power supply light up? Will the notebook boot on battery power?
I saw your reply to this issue. Mine is similar.
My Inspiron 1721 shut down and will not turn back on. Absolutely no lights or noises when the power button is depressed. All five LED's on the battery are lit constantly. When I push the battery check button three of the five (every other one) flash several times, then the lights go out and then a couple of seconds later all LED's relight. The power supply works fine (tested on another Dell), but when I plug it in (with or without the battery installed) the light on the AC Adaptor goes out. It will reset once I pull the plug and then plug it back into the wall. Any ideas on what the problem may be?