Well, by googling your computer and navigating HP's site, I found this hardware guide [PDF] and on page 1-2 it lists the compatible processors. They're all Pentium m processors, which would be a different socket even than the early Core Duos if I recall. So I'm going to say no. It's really tough to upgrade laptops as there's not a lot of room for additional cooling. Even if they're voltage compatible and would run cool enough, big OEMs don't offer a lot of bios updates to add processor compatibility.
Edit: I'm also pretty sure this would be the chipset it would have, because that's what my Dell from around that time had and the supported memory is the same for your HP. It only lists Pentium M processors.
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