There should be a file for the Windows Media Player playlist (with an *wpl file extension). You can edit it with text editor (Notepad works) to change the directory identity of every song, but it's probably just easier to try to trick it into thinking its still in the same location rather than edit the code for it manually.
If you rename your drive (and directories) to match your computer, you can resave the playlist and bingo, it should work on your other hard drive.
If you do want to do it manually, open the file in notepad. Look at what the name of the old directory was. e.g.
media src="..\Music\Top\CD 2\day of fire.mp3"
determine what the new directory for your music is. eg:
"C:\My Music\New computer\Mp3\CD2\day of fire.mpg"
Then in notepad, press Edit->Replace. Select the name of the general folder from the first instance "..\music\top\" and replace the text with your new location "C:\My Music\New computer\" --- replace each instance and test it out. If you've done this successfully, it will work