You can't transfer song files from iPod to computer using iTunes, except for songs purchased from the iTunes Store (and you can also re-download purchases from the iTunes Store Purchased screen). However, there are third-party methods and utilities that can transfer from iPod to computer. If you do a Google search on something like "ipod transfer," you should see some links.
Luckily, you are going from PC to Mac, because Macs can read the Windows disk format. If you were going from Mac to PC, it would not work because Windows cannot read the Mac disk format, so you would lose whatever is on the iPod when it got re-formatted for use with the PC.
Once you have the song files on your new Mac's drive, you can add them to the iTunes library by dragging the files (or the folder containing the files) to the iTunes window.
It does not really matter if the song files came from CD or they were downloaded, as long as they were playable in iTunes.