Try powering it off and removing the battery. Then plug it in and see if it will boot that way. Sometimes a battery can cause this. How old is the laptop? Batteries usually don't last more than a couple of years.
It was plugged in, but not charging - and eventually died. I ordered a new power supply thinking there was something wrong with the old one, but it still won't boot. We took the laptop to Staples who wanted $379 to fix whatever's broken or $279 just to recover the data on his disk. Thought I'd poke around to see I could get some help before spending a bunch of $$.. Thanks for any guidance!