iPhone 4s not charging 9/10 times
Battery certainly could be bad, but there are some other common areas of failure. 

If you shine a light into the 30-pin connector, check for any physical obstructions such as pocket lint, scraps of paper, I've even seen staples and gum. If you spot it, try to use compressed air to get it out. 

Also look for any burnt (blackened) pins which could explain it. 

Lastly look for signs of liquid. Liquid LOVED getting into those docks. Signs of liquid include corroded (green) pins, or tripped (red or pink) liquid contact indicator. The liquid indicator is in the center, under the connector plate.

Barring any of those things, it's most likely either the battery or the charging circuitry.