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...
After replacing the Dock Connector Cable you may find your iPad stuck in Recovery Mode, this is due to changing the WiFi chip (Included on the Dock Cable), the WiFi address is different and cannot be recognised. Just Restore in iTunes and all will be ok.