My iPhone 4s will not charge

This has nothing to do with the iOS 7 update--I have had it for a while. I can't figure out why my phone won't charge. I plugged it in last night, and it worked just fine. No issues whatsoever. Today, my phone will not charge. I will plug it in, and it will give me the red battery icon to indicate it is plugged in. Then, it will gain some power (bouncing between 1-4% sporadically and not in any order) without indicating a charge or registering on any devices I have it plugged in to. It will then lose power and die, and I'll have to try again to get the 4% back. I have tried restarting it to no avail, as well as ensuring that the USB port on both ends is clear of any blockage.

I tried to contact apple support, and they sent me an email asking me to click a verification button that was just font, and not actually anything that linked me to any sort of help. Does anyone have any solutions?

-Dav