An Apple ID (the "iTunes account") is an email address, but you should lbe able to sign in to Apple's services (such as the iTunes Store) using it, even if the email address itself is not currenly being used as your email address. It's just a way for Apple to initially set you up with a unique ID (without you having to try a bunch of user names that are already taken), because an active email address should be unique.
There needs to be some clarification here. When you say,
How do I get all the music off of the old itunes account...
do you mean off the iPod and onto your new computer? Except for music you purchased from the iTunes Store (see NOTE below), the "old iTunes account" (your previous Apple ID) is not relevant. There is no connection between your Apple ID and songs in your iTunes library, for songs that were NOT purchased from the iTunes Store. Your songs are simply stored in your computer's iTunes library. If your old computer is gone, and you did not make a backup of the song files, those song files are also gone, except maybe for the songs on the old iPod (if it was synced to that library). So this is really a matter of off-loading songs from your iPod to your new computer, correct?
Once the song files are on the new computer's drive, you can add them to your iTunes library. Once they are in your iTunes library, you can then sync the songs to your iPad.
You cannot transfer song files from iPod to computer using iTunes (except for iTunes Store purchases). However, there are third-party methods and utilities that can transfer songs files from iPod to computer. If you do a Google search on something like "ipod transfer," you should get some links.
NOTE: Songs purchased by you from the iTunes Store can be re-downloaded on your new computer at no cost. To do so, you sign in to the iTunes Store with the Apple ID used for the purchase. From the iTunes Store Home screen, click on the Purchased link under QUICK LINKS. On the Purchased screen, you can find and re-download previous purchases to your new computer's iTunes library.