My iPhone 4S will only take a charge from my computer. Why?

Means you computer USB is too weak to charge the iPhone.

Charge using the Apple wall power adapter.

I had this issue with my son's 4S for serveral months and we tried everything, even bought a $50.00 charging case. Last week I factory reset his phone and upgraded from ios 6.1.2 to 7.1.2 and now it will charge from the wall, computer and the charging case. I don't know why but this fixed the issue for us.

Make an appointment to bring the phone into an Apple Store if you have one nearby. They will troubleshoot the issue to make sure it's not your cable or AC Adapter. If it's not a hardware issue, then a factory reset of the phone may be in order to fix whatever issue is causing it to refuse the AC adapter's charge.

Best of luck!