Have had trouble restarting iPod touch 4's after LCD replacement, sometimes when they've got stuck booting have used this method poster by another user to get them booted -
"If you get problems powering up after screen swap, locate the 3 battery terminal beneath the metal cover, locate the +3.7 volt terminal using a multimeter (from memory its the one on the right as you look at it ) short this terminal briefly to ground ( the metal plate sorounding the home button will do ) then plug into charger and withing seconds you should get your confirmation beep and then screen shows charging, wait a min or so and it will boot up"
don't know if it will fix it but worth a try...