I've only encountered a few instances in which a laptop is unresponsive from other than an actual hardware failure. These do have a BIOS battery which can die but the trick I've sometimes used is to remove the main battery, press and hold the power button for about a full minute, reinstall the battery, connect the power adapter and try again. If this doesn't work, you have a hardware failure. I am presuming you've already tried using the power adapter without the battery installed.
Have a hp62 with W7. Led for the power adaptor works (changes to amber when battery inserted) and the led for the caps lock blinks - 2 rather rapid blinks - about 3-4 pause and repeats the 2 blinks. I hear the fan initially.
Have cleaned the unit (was not dirty), reseated the memory, did the "depress windows key, B key and hit the on button". I post here every so often - I repair seniors computers as a service and mainly deal with software issues. I'd love to resurrect this unit, so I can replay someone's old xp.
Have heard this model often has cold solder joint issues - that is beyond me - any thing I am game.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic