Is/was failing or has failed?
If the old computer still runs one of these methods may be best.
Method 1
- Backup the library with this User Tip.
- Restore the backup to your new computer using the same tool used to back it up.
- Deauthorize the old computer if you no longer want to access protected content on it.
- Keep your backup up-to-date in future.
Method 2
Connect the two computers to the same network. Share your <User's Music> folder from the old computer and copy the entire iTunes library folder into the <User's Music> folder on the new one. Again, deauthorize the old computer if no longer required.
I'd recommend method 1 since it establishes an ongoing backup for your library.
I don't have personal experience with iTunes Match, but in principle you should be able to download all the tracks currently registered to your iTunes Match account. This isn't quite the same as restoring your previous library exactly as it was. There is always the potential for iTunes match to provide the wrong version of a song and could be content such as movies, podcasts, audiobooks etc. that would have been excluded.
tt2