Q: is it possible to transfer my whole music library from my ipod classic to a new computer?

Hello there Alex-B,

It sounds like you have your music on your iPod classic and want to get it onto your new computers iTunes library. You can use this article to transfer your iTunes Store Purchases:

Re-download or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer

For non purchased content, or content from other sources please note this:

​​This feature works only for content bought from the iTunes Store. Any items that you imported from audio CDs or received from other sources won't copy from your device to the iTunes library. However, all podcasts from your device's Podcasts app and copies of all PDFs and books from your device's iBooks app will transfer to the computer. Learn how to transfer media to your iTunes library.

Thank you for using Apple Support Communities.

All the very best,

Sterling