Hello Gus Graham,
It sounds like your phone is not charging when connected to the USB cable that came with the phone. I recommend the steps in the following article named:
iPhone and iPod touch: Charging the battery
http://support.apple.com/kb/HT1476
If your battery doesn't charge, or if your device shows a low-battery image, black screen, or "accessory not supported" alert, follow these steps.
- Inspect the connector at the bottom of the phone:
- Make sure that there are no bent pins in the connector.
- Make sure that the connector is free from debris.
- If there are bent pins or debris, please contact Apple Support.
- Otherwise, continue troubleshooting.
- Make sure that the outlet you're using works.
- Make sure that the Apple USB cable and Apple USB power adapter work.
- Plug the device in to power and let it charge for up to 30 minutes. If you don't have an Apple USB power adapter, try connecting to a computer's high-power USB 2.0 port (not a keyboard). The computer must be on.
- If the device still exhibits an issue, try turning your device off and then on again while connected to power.
- If the issue is persists, please contact Apple Support.
Thank you for using Apple Support Communities.
Cheers,
Sterling