Unless the music on the old computer was purchased from the iTunes Store it will not simply appear on the new computer.
If you have a backup of your music from the old computer, you can copy that onto the new computer and then add it to your iTunes Library. If you do not have a backup, or for any music that was not backed up, you will need to go back to the original source that you got it from:
- if the music on the old computer came from other online digital stores, such as Amazon or Beatport (to name but two), try looking at your account in that store to see if you can download the music again
- if the music came from your CDs, you will have to copy from the CD into your new iTunes Library