Looking for something better too. I have been using the 3M clear ones for a while with mixed results, it helps to clean the old adhesive off, but even then it can be hit and miss. I have ordered some of the black pre cut ones today for the iPad 3, will see how they fare.
Maybe my tape gave it just enough lift for mine to work, the pic attached is the old one with the black fabric tape in the position i tried to emulate, scuse the cat hair, i just dug it out of the bin!
I had this problem and managed to fix it. The issue seemed to be with a set of contacts on the new digitizer, they had a piece of the orangey tape over them, which i removed. Do not remove this. On the original, broken one, it had black fabric tape over the copper contacts. The contacts are to the left of the home button when looking at the back of the digitizer, they are both on the home button ribbon cable, one is rectangular and one is square. I put standard electrical tape over both of these and it appears to have fixed the problem.