HI was your phone running IOS 5? The new screen units out of China have a new IC fitted on the lcd. If this new type screen unit is fited to a phone running ios 5.1.1 for instance then not only doesnt the screen work at all but the phone wont boot up either! I have had this problem with new 4 and 4s screens from 4 different sources , im lucky that i keep a fair few and have been able to use old stock screens or have been able to update the phone software on such phones using the old screen unit before i change screen. You can verify that this may be your problem, unplug both lcd and digitizer plugs . (disconnect battery first , then plug back in after)then plug phone into p/c after awhile the phone should be recognised by itunes etc. If this is the case your old screen probably totaly failed when removing. If you have no other screen units available and you think you were running ios 5 etc and you were not using it because of jailbreak etc. IF you havnt a backup of your phone then you still should be able to get one without the screen plugged in, if you had a password on your phone it would be harder , you could try just pluging digitizer plug in and guessing where the keys for your password are so you can get passed it to make a backup.
You should be able to get software update with screen unit disconnected by doing this. Make sure phone is off by briefly unplugging battery then plug back in. Hold home button in and connect to p/c via usb cable. Wait to the phone is detected in recovery mode. Restore the phone. When it says its complete, disconnect from pc . Unplug battery, connect screen and plug battery in see if you have solved your problem. Good luck.