Is it safe to assume it's a HP NC4200?
What OS are you running? Pretty sure these came out of the box with XP.
Try booting in safe mode, go to start, run and type in msconfig. Have a look under the startup tab and have a look for things you may not recognise or things you don't want starting up, and uncheck. If you don't feel confident, don't mess with it too much.
Have you recently installed something or done a software update?
How much memory is in there? Remove the memory from the bottom of the laptop if there is any and see if it boots up. If not, then try the memory under the keyboard. Replace with the other one and test.
To get at the memory, download the maintenance and service guide
http://h20000.www2.hp.com/bizsuppor...n&cc=us&prodSeriesId=447354&prodTypeId=321957
You want pages 105 to 118 for removing the keyboard. No need to unplug the keyboard so long as you can get at the memory. Just be gentle with the keyboard.
Bear in mind this is all assumption. If you've got your data all backed up it might be worth trying a fresh install or restore.
If there is anything majorly wrong it's not economically viable to fix it really.