3g battery indicator always on red

Gave my young son my old 3g to use as ipod. Fully charged the battery indicator always shows the red last 20% or so portion of the charge when in fact it's fully charged. Tried running it out and fully charging....same thing. Tried soft reset...same thing. Any advice appreciated.

Fully drained the battery again then fully charged it (I assume since it was on charge 4 hours). Battery indicator still shows red/low battery. ????