It's not asking for my me.com sign on.
Yes, but if you want to log in to your full MobileMe account, your MobileMe account email address (ending in @me.com) is what you have to enter.
When you go to me.com, what is the graphic displayed at the top?
Is it a white cloud with 4 iOS devices behind, or is it 6 icons of mail, contacts, calendar etc.?
As you type your MobileMe email address, when you get to typing @me.com the graphic should change to the 6 icons.