Busy days. I had to suspend this problem for a while but one day I will come back to this problem. BTW. I dont think it is battery problem in your case.
I tried 3 times and I destroyed all of them. But it is not impossible. During last try I unsticked about 3 quarters of screen when it cracks. I should have been more patient. Firstly I used too much heat. Screen went black. Secondly I tried toluene but it melt downs more things then just a glue.
Last time I used metal string and 100C heat. Heat it up and move a bit with the string,heat it up and move,etc. If you will succeed let me know. I wish you good luck.