iPhone 3G battery wont charge and wont connect to itunes

I have an iphone 3g which has been completely stripped down. I have put a new screen in, new power ribbon and new dock connector.

The battery is not new.

When I plug phone in to the mains power it switches on, it shows the charging icon next to the red battery icon (indicating that it is receiving power).

The phone then boots up on its own to the operating system and shows the red battery icon at the top but no charging icon. iphone reports battery is only 20% full. If i leave it on charge it does not recharge the battery.

When connected to the PC the phone is not recognised at all (no USB connection beep from phone or PC) and of course itunes does not display any phone connected, nor does Redsn0w or Tiny Umbrella.

If I try and do anything on the phone, like enter the settings the phone switches off.

I have just replaced the dock connector and verified the cables are connected properly. The logic board is fixed properly to the battery (from what I can tell).

I have done some research but as yet cannot find an answer, only to assume the board is faulty.

I have noticed some people selling fuses for the board. Does anyone think this could be the problem?

USB connection and itunes work fine (tried with a different iphone), mains power works fine (checked with other iphone).

The only thing I haven't tried is a brand new battery, which I do intend to dom but what is confusing me is the lack of connection to the PC, which makes me think the battery is probably ok.

So to recap:

Wont charge from PC or mains.

Switches itself on when plugged in to mains.

New dock connector installed.

All connections cleaned.

Any ideas anyone? could this be a fuse?