How to import non-purchased content to a new PC?

I have an iPod Shuffle 4 full of songs from CDs and would like to put the music on a new laptop. Trying to sync is resulting in warnings that music on the ipod will be REMOVED to match it with the PC(!!) Please help?

The OS is Windows 8, with the newest version of iTunes. I've tried 'add file to library' (which brings up a new window for browsing, although I don't see the device listed). Also was going to drag&drop from the device list to My Music but the list is greyed when I try to select songs (and there's no header option for My Music directly anyway.) It was very easy to transfer purchased content, interestingly enough.

Lastly, I did read 'Manage content manually on your iPhone, iPad, and iPod' and was going to try it but it seems 50/50 that I can get music transferred OFF the device and I'm not sure I still have copies of the music on my old PC as backup.

If you have any ideas please let me know. Its dismaying to think I would need to buy a separate storage drive just to transfer from one PC to this one.