Does the fan spin up at all? Any beeps coming from the laptop? My first port of call with something like this would be to check that the CPU is seated correctly - locate it, remove from socket and plug back in again. As above, could also be a fault with the motherboard but I'd give this a go first.
It may be an issue with the graphics chip if it's a nvidia g94 or similar. Get in touch with the point of sale if it's less than a few years old, they should really get it sorted if that's the issue as it's an inherent fault with these machines. That's if HP won't take care of it.