Yes, you might be able to do that, because HP uses Asus boards, many of which are standard models. In fact, a better solution might be to buy the SAME HP board on eBay, as the HP version is CHEAPER than the Asus version.
Also, for a few years now HP has been using soldered in BIOS so you can't do what you're talking about. So if your board is old enough and a standard model, you might be able to swap BIOS. Otherwise you can't.
I have an even better solution: Screw the Restore disk. Get a copy of the OEM windows CD for your windows version, and use your old licence number to do a normal load on the new board.
Also be aware that even full ATX HP cases normally come with mATX boards, so they use the lowest rear mount for mATX boards. Many full ATX boards don't use this mount. So if your case is full ATX and you have the extra mount grounding it, make sure you unground it first by covering it with some good electric tape.
<font color=blue>Watts mean squat if you don't have quality!</font color=blue>