|You say it's not recognizing the drive case. I'm not sure if a USB port will recognize an empty enclosure connected to it (if that's what you're trying). It should however recognize the drive in the case.|
Does the hp recognize a regular IDE hard drive in that same case; that is, is the problem with the external case or the LS-120? If it's the case then you need to try another.
What USB version does your HP use--2.0 or 3.0--and which version did the xp machine use? I had a problem with an old flash drive that was recognized on an XP computer but not seen by a windows 7 laptop. I never figured out the reason and ended up buying a newer one that was seen by both. Maybe something like that is the reason for your problem.
If all else fails and you really want to connect an LS-120 I noticed there's there's some external USB LS-120's on ebay.