I had a Surface RT with a broken digitizer.
Purchased a used digitizer lcd assembly (frame included) from ifixit. The part arrived quickly and in great condition. It took me about an hour to transfer all the parts to the new screen assembly and now it's working like new again.
Before ordering the new assembly I tried using a heat gun to remove the digitizer. It is a very time consuming and tedious process, I quickly determined that it was not worth the hassle. The used screen that I received was in excellent condition and a huge time saver.