You said that the harddrives (new and old) worked in another system just fine.
Some details as to how you connected it to the other system would have been nice...

1) make sure that the WD hdd has the jumpers set correctly....WD HDD must have the master...no slave jumper set or it must be set to Cable Select...dependent upon your computer configuration. If the jumpers are set in the wrong configuration they will not show up...
2) Also a new drive must be set-up before it can be seen by the computer...there is a utillity diskette that should have come with your new drive. Install the drive and then boot to the utillity disc and set-up and format the new drive with the diskette program......this surprises me as you noted that it ( Both drives) was seen in other computer...after a drive is set to 0's (wiped) it can't be seen without going through the set-up process,
3) if the WD drive replaces an EIDE drive then there are no third party controller drivers to install as XP will see it as a legacy hardware during the operating system installation and install the generic IEDE controller drivers

4) there must be a bad connection in installing the harddrive as it is not being seen...or the drive has not been properly set up.

5) there are no IEDE controller drivers for the laptop in the drivers section of HP because they are installed during the installation.

6) If you had gone to HP and actually looked for the driver downloads you would have noticed that there are different versions of that model and you failed to inform us of all the details to help.