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Hi, Did you solve this issue?
I've had a similar issue with a 4s I just bought off ebay.
normally on screen changes i follow same as everyone else:
1. Power + Home button reset
2. check connections
3. check lcd in another phone verify it works
these didn't work this time, although similarly like you i tested the replacement first and had it come to life once reset. but then nothing when put back together.
Took it apart and checked it over but couldn't see anything wrong (all connections fine and no piched cables)- when plugged into my mac it would be recognised by itunes and then the charging beep would happen every few seconds. From the other side the backlight would come on. Oh and the board would get pretty hot too.
looking over the board under magnification there was a slight sign of water damage near the lcd connector. (indicators were still white and was told it had only been dropped so wasn't my first thought) one of the 4 tiny components between the two lcd connectors was missing due to corrosion (top left one) cleaned the board up and soldered a jumper between the two pads and it powered straight back up no problem and no heat issues anymore.
Just have a close look to see if anything might have been knocked off the board when changing the screen.
Hope this helps someone out.