Hardware

plus, betcha new drive wouldn't boot either based on your description of the problem. sounds like ide bus failed on the laptop?
and to try to answer question about non hardware specific install of windows xp home, don't think you can get away with this very easily. because the HAL might be very different from laptop to desktop. You can force a HAL (see the mskb at support.microsoft.com. during the install but...
can't you check out the laptop ide and other stuff with hp diagnostic utilities? this is the route I would take. if the drive proved to be the bad boy i'd buy a laptop hard drive 'tray' that would allow me to use the laptop in a desktop then i'd use the utility software provided by the drive manufacturer to copy the old drive to the new drive. when you buy the 'tray' have your old laptop drive with you or the model number in hand as you will need a tray with a matching ide bus - different in Laptop Land.

You can slave the laptop to your main hard disk and Windows should assign a drive letter to the 2nd hard disk and therefore be able to access files on the laptop disk.

Ideally you would install Windows on the hardware you want to use it on and not a completely different system which may not boot due to different HD controller or HAL.
Using Sysprep tool from the Deploy.cab file from XP CD can remove most of the hardware specific stuff but its not guarantee it will work on another PC.

but I agree with Sgt. that it sounds like the controller for the HDD's is going out. Here is a test

Boot to a floppy disk, can you access the HDD, CD drive, etc.?
If not, then slave the drive on the second computer and backup your data. Send your notebook in for repairs.