These are two possible approaches that should work to move an existing library to a new computer.
- 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.
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.
Both methods should give the new computer a working clone of the library that was on the old one. As far as iTunes is concerned this is still the "home" library for your devices so you shouldn't have any issues with iTunes wanting to erase are reload.
I'd recommend method 1 since it establishes an ongoing backup for your library.
Should you be in the unfortunate position where your computer has died with no backup then see Recover your iTunes library from your iPod or iOS device.