2nd Replacement LCD not working.

take a look at the dock/connector 4, it may be not lodged properly. i take it that if you are replacing the lcd you have dropped it? if it has been dropped at the bottom sometimes the dock is damaged and therefore there is no way of power getting to phone/battery and itunes can't recognise phone. it may be that the battery has now run out of life because it can't charge via dock-hence your short screen life, which now shows nothing. clean dock port with isopropyl alcohol, look for dust/dirt in bay. check ribbon 4 is connected properly. the other problem may be that battery connection is dislodged....check under the "don't remove" sticker. maybe the prongs that make connection with battery have been damaged. if so you can try to gently pry them up. dock connectors are fairly cheap to buy.