[rage=nuclearpowered] HP's have crappy PSU's and crappy motherboards (and crappy RAM, and crappy GPU's, and crappy, ODD's, and...

)
The motherboard may be failing to POST (or some other motherboard issue) or the PSU may be failing to power the system properly, however I'ma put my money on the motherboard the way it sounds. Unfortunately since HP only uses crappy components it's hard to suspect the least crappy piece of hardware as being faulty as it's all just one big pile of crap stuffed inside a halfway decent looking case.
My first PC was an HP BTW. Damn that thing was a piece of crap... oh and don't even get me started on their crappy tech support that tried to swindle me out of $100 on a PC that was
1 single day out of warranty to fix a fatal error message that they no doubt programmed in the piece of crap... couldn't ever get the system to enter sleep mode reliably nor could I get any screensaver to work on their crappidy crap crappidy!!!
Dealing with that HPiece of crap is what gave me the motivation to learn how to build PC's, thank you HP for that! [/rage]