iPhone stuck on black screen and won't restore...

My iPhone screen will stay black until I plug it in, but when I plug it into iTunes it says the phone is in Recovery Mode and the phone needs to be restored. When I start the restore and update process it goes fine until it gets to the "Verifying iPhone restore with Apple..." than immediately following the restore stops and says "iPhone could not be restored. An unknown error occurred (2001)" than starts everything all over again. Does anyone know why my phone is doing this? And is there a way to fix it? I have tried on 3 seperate computers and tried holding the home button while going through the process but it still didn't help. Please help!!