iPod Touch 4G and Messages, FaceTime and iCloud Backup

Does Messages, Facetime and iCloud Backup still work on iPod Touch 4G? Just recently my iPod Touch 4G shows me the Get Started screen from Messages and FaceTime and wants me to sign in with my Apple ID. However, even though I'm positive I'm entering my Apple ID correctly my password is rejected. Same for iCloud backups. Last one I know completed was on January 7th.