Thanks for your quick reply!
My Ipad has a small SIM card slot on one of the long sides (empty) and a black strip on on its top just like you describe it. So then it must be a G3.
But I don't have any 3G tab in my settings. There is a tab called "Cellular Data" which is greyed out (No SIM) and which I can't access.
I got it in June, so if this is not an easy thing to resolve, I think I must be able to get support from Apple.
Would you have any other suggestions before I do that?