It sounds like the iPod needs a Restore using iTunes. But you're saying iTunes does not see the iPod, even though Finder sees it, so if iTunes does not see it, you can't do a Restore. It definitely does not appear in the iTunes sidebar, under DEVICES, correct?
I just did the following with my 5th gen iPod nano and Mac (just to confirm it does no harm), so you can try it, if you want. This procedure will erase the nano, so I hope all the songs (and other content) on it now are all synced from your Mac's iTunes library. I have previously done this with older "hard drive" iPods before, but not a nano.
Put the nano into Disk Mode, as before (link in previous post).
With iTunes NOT running, run Disk Utility and connect the nano. The nano should appear in the Disk Utility sidebar. Select "Apple iPod Media" in the sidebar, NOT the iPod's "volume" that is indented under it (so the DEVICE should be selected, not the device's volume). Over to the right, go to the Erase tab.
Set Format to Mac OS Extended (Journaled). You can Name it whatever you want, or leave it "Untitled." Click Erase. This will erase (reformat) the iPod's flash storage. Because the DEVICE was selected in the sidebar, it will also re-partition it (to one partition). It should take less than one minute to complete, then Eject the iPod. It should say OK to Disconnect on nano's screen. But you don't need to disconnect it.
Use the Reset procedure (link in previous post) to take the nano out of Disk Mode. Run iTunes. Hopefully, iTunes will see the iPod (in "recovery mode"), and offer to Restore it. If you can then Restore it successfully, your nano should be working properly again.
NOTE: If there is a hardware problem with your nano, erasing it with Disk Utility may not work. And that will leave your nano non-functional.
