Charges When Off, Wont Charge or Recognise by Computer When On

Hi Guys,

Just wondering if anyone could help, ive got an iPhone 3GS 16Gb Here, that originally would not boot up, furthur more the power button was damaged and the screen was cracked.

Firstly I replaced the Power button and Ribbon and then the Glass, this went smoothly was able to get the phone up and running again by re-jailbreaking (it was originally jailbroken apparently) So the data is still intact.

This is when i noticed the problem; the battery would not charge when the phone is on, neither would it be recognised by my PC.

Naturally I replaced the Battery and Dock Connector; just to cover both basis. Heres where it gets wierd from what i noticed

1. It WILL charge if the phone is turned off.

2. The phone IS recognised by my PC in DFU mode.

3. The Battery will not charge, nor will the iphone be recognised by the PC when on.

Just wondering if anyone has encountered this before. It seems like a software issue, and yes i can do a restore in DFU mode, but im trying to keep the data intact and i cant make a backup as it does not recognise when on.

Any advise.

Appriciate any help, Thanks.