iPhone 4 Won't start after screen replacement

Hi!

I have changed many Iphone screen already and never had a problem that I couldn't solve by myself or with help from here.

This recent screen replacement is really weird.

I changed the screen and put everything back together.

Iphone was "dead" nothing displayed on the screen.

I tried charging did not help.

I teared it down just enough to connect the old screen back to motherboard.

It starts without any problems?

After that comes the tricky and crazy part, disconnect the old screen and reconnect the new screen (WITHOUT powering phone off while doing it).

Now the new screen works like a charm.

BUT!

if I turn the phone off... it wont start again if I don't do that "old screen new screen" trick again...

Or it starts but there is now image?

What I should do?

I have checked the connections and the phone worked like a charm with a broken front and back glasses.