I had a HP Compaq 6715b laptop lying around which I thought was dead. When pressing the power button, nothing happened, not lights, no beeps, nothing at all.

I came across a hint which seems to be a well-known fix for such issues: unplug the power cord, remove the battery and press the power button for a long time (I did it for around 30s). Afterwards, I connected the power cord without putting the battery back in. Surprise, surprise: the laptop powers up without a problem (after having reconnected the hard drive which I removed ages ago to copy the data).

If this really fixes the problem for good will have to been seen. There are reports on the internet about low-quality motherboards (especially power connection) in the HP laptops of this generation.