I can log into iTunes and App Store but NOT iMessage. What gives?

I'm currently using Wifi with my 3rd gen iPad. iOS 6.0.1. I'm not home so I don't have access to my iMac (actually currently at 30k ft somewhere over Virginia :) ).

Anyway, I can log into iTunes, access the App Store, sign out of those, log back in. No prob. I used my appleID and pass to write this message. But I cannot get into Imessage, and I can't figure it out!

I get an error saying: "could not sign in. Please check your network connection and try again." If I try to make a new appleID, imessage thinks and thinks...nothing happens.

This isn't a new issue, it's been like this for quite a while, since upgrading to iOS 6 months ago. How can I get into imessage on my ipad? For what it's worth, it works fine on my iPhone.

Would appreciate any help!