Can I save My music on a dead Motherboard

Based on the age of the iPod, they’re probably FairPlay .m4p files or 64-128kbps Limewire files. The FairPlay files are encrypted and you need to know the Apple ID to decrypt them and get the key. When it comes to Limewire files, the files were usually low bitrate because a lot of players at the time basically had low storage due to the cost of NAND flash. The iPod and Rio (HD based) players were the only ones with lots of storage at the time, but you paid a LOT MORE for them.

Unless you know the Apple ID or can crack the FairPlay encryption and extract the keys from the iPod, you can't save those. Limewire files are usually more trouble then they're worth.

Your best bet if you really, really wanted to is to move the flash chip to a matched capacity Nano from the era, but these are also prone to battery issues and a lot of them exploded or were replaced with later models so it can be quite hard to find one to transplant the chip on. Your best bet is to pick the ones you want the most, buy the CD with it and then rip it so you truly own the songs without purchaser metadata as required by the record labels or more DRM.