Q: i was using my 1st generation ipod nano

A new iTunes install should not remove the music library unless the install was incorrectly applied. There is no way to recover the music from the Nano.

The iPod probably had data corruption, and may require you to do a Restore using iTunes

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

This erases the iPod, reinstalls its software, and sets it to default settings.  Before erasing the iPod, is it still accessible on the computer (outside of iTunes) as a storage device (with disk use turned ON)?  Do you use a Mac or Windows PC?

Your current problem description does not sound like a clarification of your original post.  That error message is not about data corruption.  It usually means your iPod is currently formatted for Mac.  That's why it currently works fine when you play songs on them, because there is nothing wrong (if you're a Mac user).  Windows cannot access the Mac disk format, so iTunes needs to do a Restore on the iPod to reformat its storage for Windows.  There are some software products that allow Windows to access Mac-formatted storage, but I'm not familiar with them.

NOTE:  Even if the iPod is formatted for Windows, you cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from the iTunes Store).  By design, iTunes syncing is typically in one direction only, from iTunes library to iPod.  However, there are third-party methods and utilities that can transfer from iPod to computer.  If you do an Internet search on something like "ipod music transfer," you should get some links.  So, maybe (?) you can first get the software that allows your PC to read Mac-formatted storage, and then use a third-party method or utility to transfer song files from iPod to computer.  THEN do a Restore on the iPod to reformat it for Windows and sync to your PC's iTunes library.

If the iPod is not formatted for Mac, Windows thinks it needs to be formatted for some other reason.  That message you described ("windows needs to format the device for it to work in windows") sounds like it came from Windows, not from iTunes.  If the iPod is still functioning properly (as an iPod) and playing its music, you may want to connect it to another computer, as a test to see of the same message appears. 

NOTE:  "Another computer" can be a Mac, because Macs can access the Windows disk format.

Make sure you do not sync it with an iTunes library or do a Restore if prompted, because those actions will erase the iPod; don't even run iTunes on that other computer.  But IF the other computer can access the iPod without an error message about needing to format its storage, use one of the third-party methods or utilities to off-load the iPod's songs there. Then, transfer the song files to your computer and add them to your iTunes library.  You can then connect the iPod to your usual computer and trouble-shoot it there (including doing a Restore in it) without concern about losing your songs, because its songs are now in your iTunes library.

Going forward, you should back up your complete iTunes library, in case your computer or its drive fails.  Here's how you can back it up to an external drive

Manage and back up your iTunes media library - Apple Support

An iPod is not designed to be your iTunes data backup, and it's risky to only have your songs stored on an iPod.  It can break, get lost, or have data corruption (requiring a Restore).