You may Sync Programs, and yet skip syncing Songs.
You need to take a close look, on you iTunes what you asked it to Sync.
If The original Songs are no longer on the iTune library, and you instructed iTunes to Sync, it is as if you asked iTunes to delete all songs from the iPAD.
Do you have you NEW song running OK on the iPAD, or nothing at all ?
I the iTunes is not supposed to Sync Songs. And yet you can't see them on you iPAd Application, Try a full restart on the iPAD before you start any troubleshooting on the iPAD.