When it dropped it probably ripped/tore the digitizer cable. Those things are very very delicate, and with the screen hanging off by just that cable I can almost guarantee that it damaged the cable. My suggestion would be to put a new screen on the device and make sure you glue it down next time. Once you glue it down and let it cure with something heavy on top of it for 24 hours like a couple books or a stack of magazines you shouldnt ever have any problems with the screen coming loose. I use the 3M adhesive strips specifically cut for the itouch 4th gen and they work great. i buy them on ebay for less than $3 USD and it comes with 5 of them.
@genesis rubio. I'm almost positive you have a defective display. Same thing happened to me and i connected the old screen again and it worked fine. Sent the display back that was giving me the white screen and they replaced it with a different display and it worked like a charm. I would suggest exchanging it for a different one and i would be willing to bet that works.
Fixed the issue. I took it apart and checked all the connections again and all the sudden it started being recognized with itunes and the computer but all I had was a white screen. Hard reset did not work either. Turned out the digitizer was defective, sent it back and they replaced it with another one and it worked perfectly.
I was having this same problem and after messing with it for a few days i finally got it to display a white screen. Before this it would not power on, or be recognized with itunes. I tried the hard reset and it did not work. Tested it with itunes and with the white screen it was recognized. Couldnt get the white screen to go away for the life of me. Until i figured maybe the LCD was bad. Exchanged the LCD for a different one and got the white screen AGAIN... hard reset worked this time (power button and home button til ipod reboots) and it booted up just fine. I think the problem I had with the original no power was just not having a connection sealed all the way. It looks and felt like they were but after taking apart and making sure all connections were snug it finally powered back on. Try connecting it to a wall charge via A/C and see if you get a result doing that.
I finally got mine to SOMEWHAT work. After disconnecting the new digitizer and re-installing the old one it seemed to work just fine (to my relief lol) so I then un-installed the cracked digitizer again and re-installed the new one and still same problem, no power and wouldnt be recognized by the computer. So I started messing around with the connections and finally got it to display a white screen and when plugged into the wall charger it would make a beep. Tried a hard reset because I've had the white screen issue before and solved it with a hard reset. Upon trying the hard reset the white screen would go black after about 10 seconds, so i'm assuming the iPod was restarting, because during this time it wouldnt respond to me pressing the home button for around 10-15 seconds (boot time?) then after the 10-15 seconds when I press the home button I just got the white screen again. I'm assuming I got a bad LCD since I know the iPod is still good after re-installing the old screen. So I am going to send back...
I'm in the exact same situation as you. I replaced the lcd/digitizer last night and now it wont power on or be recognized by the computer or itunes. im still looking for an answer myself. if you happen to come across the reason please let me know. this is my 4th ipod 4th generation repair and ive never run into this issue before. i even tested the original cracked digitizer because i knew that worked and it did the same thing with that one hooked up.