works when plugged in but not on battery.

A blinking battery indicator, combined with very quick discharge time, is usually a sign of a worn out battery.

Laptop batteries tend to discharge faster after a couple of years of use, or won't hold a charge at all. Batteries that are often fully charged but left in the laptop while it's running on AC tend to wear out faster and usually won't give the laptop any charge whatsoever after a year or two.

You could go search on eBay for a replacement by searching for the model number of your laptop or battery.