syncing to a new computer

I have my Ipod Classic synced to a very old Toshiba computer. I have 40GB of music on Iplayer on the Toshiba carefully accumulated over a dozen years or so. The Toshiba is now pretty much finished and I have a fairly new Macbook Air. My problem is this, is it possible to transfer all the music from the Toshiba to the Macbook Air? I have plugged the Ipod into the Mac and the music files do appear but in a recessed font, and can't be played or accessed. I am dreading the thought that I will have to start again from scratch and start uploading all my music from CD again. Hope my question makes sense and someone has an answer.