If your old computer is still partially functional:
1. Boot your old computer: Even if it is not fully operational, try starting it up to check if you can access your iTunes library.
2. Open iTunes: Launch iTunes and sign in to your Apple ID if prompted.
3. Check your iTunes Library: Browse your iTunes library and find the songs you purchased.
4. Authorize your computer: If needed, authorize your computer to play the purchased songs. You can do this within the iTunes preferences under the "General" section.
5. Transfer songs to an external drive: Connect an external storage device, such as a USB hard drive, to the old computer. Drag and drop the songs you want to transfer to the external drive.
If your old computer is not functional or completely dead:
1. Contact Apple Support: Reach out to Apple Support and explain your situation. Provide them with the details of your old computer and your Apple ID.
2. Data recovery services: There might be specialized data recovery services available in your area that can help retrieve the songs from the old computer's hard drive.
3. Previous Backup: If you had a backup of your old computer's iTunes library before it stopped working, you might be able to restore the songs from the backup to a new computer.
It's worth noting that if you've already migrated your iTunes library to a new computer or updated to the new Apple Music app, you might find the songs in your music library on the new device.