Hi guys.
The same happened to me and I got it working by reactivating using the iAsign method for the windows.
Apparently different from the activation in for the 1.0.2, on the 1.1.1 the activation process uses the SIM card ICCID for authentication. So, if you activated using a specific SIM card, after using AnySIM, you can only use the phone for that card.
I had this problem because during activation I use a test SIM card, and after unlocking I could only use it. To fix, I reactivated with the card I wanted to use and the "Activate 1.1.1 on Windows (iASign)" method described in
http://www.iphonegoboom.com/activate/activate111.html. That did the trick for me.
Just one note. If you used this method to activate the first time, remember to use new iPhoneActivation.pem and iPhoneActivation_private.pem since they are apparently changed when you run iASign the first time.
I hope that helps you.