Thank you for posting in the Apple Support Communities. It is impossible to use your iPhone if you cannot charge it, so I would definitely be concerned about this as well. It sounds like you have tried multiple cables, which was a great troubleshooting step to rule out the cable as the issue. I found an article to help isolate the issue further:
Follow all the steps you have not already taken under "Battery does not charge from the USB power adapter" and then the steps under "iPhone displays the low-battery image and is unresponsive." The last step listed there is to reset your device:
Resetting your device
Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.
You can find the full article for resetting your iPhone here:
I hope this helps!