I faced the exact same problems with my new brand new s4 module from a official Samsung dealer. I could secure the whole frame, but once i secured the right top part of the midframe (looking from behind) it would short out and not even boot the whole phone anymore.
The phone was a i9506 and the module a i9505.
I am not sure if this has anything to do with it, but i do know what caused it.
When i taped off the black screw securing the motherboard right under the part of the frame that shorts the display the whole problem went away.
I tried it without the black screw and it also does '''''not''''' short out.
I believe the black screw helps alot with positioning accuracy from your GPS, so if it is not a solution to leave out the black screw for good, u will have to kapton tape it.
To make it a little bit more clear, i am talking about this black screw:
[image|512913]
Good luck! :)