Mine too, Best guess is shorted capacitors in power supply section of main board. Mine was drawing 250mA when off. Very annoying solution is to remove batteries unless you are actually photographing something. When possible replace the caps... I have yet to have the time to do this myself.
Remember after the cable retainer plate but before the screen is laid down, peel the proximity sensor protective film, and the tiny red tab on the camera peephole protective film.
Then you can start to pull a little bit on the thin blue strip tab so it hangs out, rest the screen clips in position but do not push down.
This will leave enough gap for you to now fully pull out the thin strip. Then click the screen down.
I had a bit of a scare, during 1st power on test screen just showed snow, super long pressed to turn it back off but there was no feedback to tell me it had done so. Un&re-plugged screen and got a bigger scare when it wouldn't turn on. Insanely super long press and it did come on to a normal boot sequence and a beautiful screen.