I have a three month old HP Notebook. With it completely powered down, the battery goes flat in about two weeks.
I've spoken to HP support, who seemed to know less about computers than I do, and simply kept changing their story as to why it might happen.
Their final suggestion was that it was "an old battery". When I pointed out that I'd had the machine for only three months, they started waffling about the battery could possibly be much older than the machine.
At no point did they come up with a useful suggestion, or an offer to try and fix the problem.
My personal opinion is that there is a fault in the design of the charging circuit, that means that when the machine is unplugged and powered down, current is charging a smoothing capacitor that its then being discharged through a resistor.
If you Google it, it seems to be a problem for lots of HP users, and nobody has an answer, except to remove the battery after powering down.