That sounds like an electrical malfunction with the power-on cable. Most likely it's trying to establish a connection but fails for any number of reasons, including a mainboard component has been knocked loose, the power-on cable has somehow dislodged itself or there's too much dust, moisture or dirt.
If your HP is still under warranty, make use of it now. If not, we're going to need some more info on the HP, like full model name and some specs.