My iphone is charging slowly?

Acouple days ago my iphone completelty shut off and wouldn't turn on just recently it did and its charging extremely slow. I have the warrenty on apple and i wanted to know if i could get the battery fixed. Also my iphone is cracked on the back but thats not the problem because its happened before but it wwould charge fine. I wanted to know if apple would still change the battery even if my iphone is crack. I have a iphone 4s and its updated to ios6

Plug it in and then power it off.
The charging circuitry runs from the firmware and not the OS - so you will either get a full charge and have a chance to reboot it in 2 or 4 hours to check on the charge status or know where the failure lies.
It's most likely a temporary CPU hog draining charge as fast as it can accumulate and a simple reboot (hold the home button, slide to power off, restart once it shuts down normally) is generally going to clear this up

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