First things first, don’t sync either of your Ipods with your new PC as it WILL wipe all of the music off them.
What you need to do is transfer all of the music off one of your Ipods onto your new PC and the way to do this is by utilising a third party software application such as idump or copypod (just google either of the names).
Copypod is a paid for piece of software which costs about $16 (£10) however I have used this program on numerous occasions with a handful of different Ipods and they have all worked fine so I can vouch for its usability and reliability.
If you want to try a free option first, then try idump or just google “copy songs from ipod free” (minus the quotation marks) and try one of the other free/shareware programs that come up (though you should note that most shareware will only copy a certain number of songs unless you buy it so they would probably be of no help).