Hi,
Double check the battery flex cable connector on the systemboard to make sure that no pins were bent etc when removing/replacing the cable.
You may have to also check that the Power button is positioned correctly.
Step.19 of the ifixit [guide|119734] shows the button for you to compare.
A new battery may only prove that the replacement is OK (did it charge to 100%?), although in saying that funny things can happen when you have power problems.
Did you try getting into the recovery menu area and check if you can start the phone that way?
Here’s a [https://support.t-mobile.com/docs/DOC-27909|link] that shows how to use the hardware buttons to perform a hard reset.
''DO NOT perform a hard reset as this will erase all your data and downloaded apps.''
The idea is if you can get into the Recovery menu area, there should be an option that says ''reboot the phone''. Use the Volume buttons to scroll to the reboot option and then use the Power button to enter.