HP Laptop won't boot, lights flicker

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My HP Pavilion ZV5000 won't start up. I press the power button and the
LED lights flicker, the fans budge slightly, and then it all turns
off. The laptop itself is one of the shakiest computer's i've ever run
across, and I have a strong suspicion there's a simple solution.

The battery light is on saying it's charged, so it's not like the
laptop's not receiving power. The battery itself is very weak (if that
has anything to do with anything). If I take the battery out it with
the power still plugged in it's the same behavior.

I would be fretting that it's some kind of permanent problem but I had
taken the laptop to a friends (and it had previously been working
great) when it started doing this. Lights flicker and that's it. I
pressed the button five or six times thinking it was nothing and it
started up fine randomly. It's not starting up this time, but it
suggests that it's some kind of easily fixed problem.

I've tried cleaning the fans, actually, and that didn't work. I
checked the simple solutions like making sure everything is getting
power, and it is. And I've held down the power button, that doesnt do
anything (the power actually turns on when you release the button, not
hold down).

Man, any help would be so great. Thank you.

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