After replace display, Asus zenfone 5 stays on only with power cable

Hello everyone! Sorry for my english :)

I have a asus zenfone 5 who fell and as a result has cracked the glass. I bought a kit for the replacement of the display and yesterday I replaced it.

The display works perfectly but there is a problem: the phone turns on only when I plug in the power cable and goes out as soon as I remove the cable. Once you turned on the phone the power and volume buttons works and the battery is detected and appears to be in charge, but without the power cable the phone is not working. I also tried to disconnect the connector that connects the battery to the phone and the phone still comes on connecting the power cable, however, does not detect the battery.

What can it be? Should I try to replace the battery? Or is it more likely that damage has a connector (does not seem to have broken anything).

It 's really weird because when the phone is connected it works and it is in charge.

Thank you