I changed the broken touchscreen today... with success, except that during the operation, I broke the LCD! (I did not read the comments first!!!) Indeed, the screen was broken in many parts and as I wanted to unpaste some of the rather small parts (1-2cm wide), they pressed on the screen and broke it. It is not visible when switched off, but I could check that some broken parts correspond to the shape of some shards of glass when I switched it on and realize that I broke it.
A comment that might be useful: when you assemble again the microphone part, extend maximally the door of the SIM and the microSD, otherwise you may have difficulties to place it back, and do not forget the connector of the proximity detector.