Chosen Solution
After replacing the battery in my 4s, the phone turned back on, I plugged in the power and the phone dinged and showed the lighting bolt up by the battery (it did not do that before the battery replacement), however is not charging. I saw another post suggesting that the doc connector needs to be replaced, prior to the original battery failing, I never had a issues and made sure the dock connector was regularly cleaned.
have you tried a different cable because you might have more then one problem since the phone is recognizing that you have it plugged up to something it could be a faulty cable. possibility of that is slim but it is worth a try in my opinion