Is the charger plugged in via a wall-wart type transformer, or a normal lamp plug?
The bulk of chargers that use the wall-wart are simple trickle chargers. The ones I've been into all had failed wall-warts, not a failure in the charger base.
The ones that plug in with a "lamp cord", or a very heavy-duty style wallwart may be "smart chargers". These generally have more than one light (mine has Charge, Ready and Defective Battery). These are typically called "fast chargers" and will float the battery in an hour or so.
Single red light out = probably dead charger, IMHO.
Put the battery as-is in the drill, pull trigger. Note response. Charge 10 minutes, repeat test. If the test result is better, the charger works.