You have to heat it up. The adhesive will not release without doing so. Take your time and work in sections.

The board sockets (connectors) are the same. The iPad 3 digitizer cable is longer though. So, as stated above, you can use the iPad 3 diggie on an iPad 2 with a couple of folds on the longer cable. However, you wouldn't be able to use an iPad 2 diggie on an iPad 3. The cable just isn't long enough. IndyElectronix

I had the same problem as well. Turns out that the little pins on the digitizer connector on the motherboard come out VERY EASILY. I'm in the process of looking for a replacement connector. You may have the same issue. Put a magnifying glass on that connector and make sure all the female pins are there.