I had what may have been a similar issue after replacing the LCD. Have you tried the "erase all content and settings" option? On mine, the iPad would power up OK, but after powering it off, the next time during powering on the Apple logo would appear, but then the display stayed dark. I could tell that the power was actually on, because I could hear the sound that plays when a charger is connected or when pressing home+power to take a snapshot. If I'd hold home+power for about 10 seconds, it would perform a "force reset" and power on and work normally, but once I shut down the cycle repeated itself. It was annoying, and I don't know what caused it, though I didn't transfer over the little flex cable with the magnetic sensors from the old display, so that might be related. Anyway, I erased all content and settings, and this problem went away. I should mention, though, that I have not yet restored the backup I made before the LCD replacement.
I had a similar issue. How did you reattach the metal bracket behind the button? I removed all of the adhesive (and the surrounding glue) from the display where the bracket attaches, and from the bracket itself, and then installed new double-sided adhesive pieces (cut to match the sections where the bracket attaches) before firmly pressing the bracket back onto the display. I did not put new glue on. So far it is working OK. Before I did all this, the operation of the button was terrible. It seems to be important that the bracket is reinstalled properly, and probably with new adhesive. There was also a little white ring with adhesive around the button itself, which I did re-use.