Hello Beanington,
Thanks for using Apple Support Communities.
From your post I understand that you have a new computer and would like to get your iTunes library loaded onto it. If you have access to that older computer, you can follow the first link below to transfer the iTunes media.
If you don’t have a backup of your iTunes library and your old computer is unavailable, you can download past purchases made with your Apple ID through iTunes in the Cloud.
If you have multiple Apple IDs, you might find it easier to transfer purchases from a device after authorizing your new computer with your Apple ID.
If you previously subscribed to iTunes Match, you can turn on iTunes Match once your new computer is authorized.
How to move your iTunes library to a new computer - Apple Support
Another option is if you have your iTunes media on an iOS device or iPod, you can follow turingtest2's information in the link below to transfer the content to your new computer from that device.
Recover your iTunes library from your iPod or i... | Apple Support Communities
Take care.