The handbook does list the supported iPods IIRC. I don't have it to hand so can't tell you which they are. I have an old iPod mini which I'm using and it works fine.
Ultimately I'd say your recourse is the dealer - they've fitted something which doesn't work. If your iPod is a supported model then go back to them.
Incidentally, to find out exactly which iPod model you have, Apple have a very comprehensive facility which allows you to do this
Identifying iPod models