"My HP dv1000 has the same problem, and so -- from searching Google -- do a zillion others'. Like many others, the fan quit on my dv1000 when quite new, so I learned how to disassemble it to fix my fan. You can find HP instructions at http://h10032.www1.hp.com/ctg/Manual/c00312379.pdf. I say this because even if the fan is working well, the aluminum duct that transports the fan air over the chip gets clogged with dust. It is filled with a fine matrix of copper wire and there is just no effective way to clean it without disassembly. Take the duct off and run water through it. Now -- about this damned power up problem -- try this. Pull the display toward you and half-close the laptop till its only open about 3". Leave yourself just enough room to reach in and hit the power switch, HOLD the screen, pressing it slightly as if you were about to close it all the way, but not pressing enough to actually close it. Why? The display is screwed to the same inner frame as the mother board. Constantly Opening the screen flexes the frame and flexes the mother board... tiny cracks can appear in the board r the solder joints.. By holding it like this you are flexing it back the other way. Does it power up now? Mine did. But as soon as you open the display, it powers down again because the cracks in the board open up a fraction. Solutions: New mother board (of course)-- an expensive solution. A soldering iron and a steady hand (and a magnifying glass) -- this is only for the brave. Try some flat nylon washers under all the rear screw holes in the mother board. They bend the board up very slightly so it is concave. I was able to get mine to boot that way after re-assembly, but I'm really not confident about opening or closing the display any more than absolutely necessary. Still at least it is powered up and useable. "
This is a quote from an HP help forum, hopefully this helps
Alright, gotcha. So it will not turn on with the power switch. If it is under warranty, I would recommend calling HP and sending it in for them to deal with it free of charge. If that is not a possibility, it seems like requiem's above post may be the best option, as it seems like a common problem in that model. If you do not know much about computer's, bring it to a repair shop or someone who knows what they are doing along with the above-mentioned advice and see what they can do for you.