iPhone 3GS screen black

My daughter's iPhone 3GS turned itself off 4 days ago and would not turn back on. I tried charging it overnight but it would not charge. I opened it up and was trying to see if any connections came loose or if there was evidence of a short on the logic board. Tried to charge overnight again, still wouldn't charge. Today, I used my multimeter to check the battery and it was only showing 2.9v so in a last ditch effort to charge it, I had my hubby plug it into his iPad charger instead of my iPhone charger. It finally charged. When it turned on the screen was completely black but the touch was working (if you hit the home button and slide where the unlock slider is you could hear it unlock). I did a hard reset and put in recovery mode and iTunes restored it but the screen was still black. I double checked all the cable connections (and made sure the logic board was off the battery) while I reinstalled the display cables. Now, the phone is in recovery mode but iTunes says it could not be restored and gives error code 29. I have tried everything I could find on the Internet (within reason) to try to fix it but nothing is working. Please help.