Diagnosis
This usually means your toothbrush isn't getting a charging signal at all. The most likely culprit is gunk build-up on the contacts, preventing a connection.
How to Fix It
First, unplug the charger from the wall. Take the brush head off. You'll see the little metal charging nub on the handle and the matching spot inside the charger base. Grab a cotton swab and some rubbing alcohol. Give both sets of contacts a really good scrub to get any toothpaste or mineral deposits off. Dry everything completely with a clean cloth. Then plug the charger back in and try setting the handle on the base again. You should see the red charging light come on solid.
If That Didn't Work
Your charging base itself might have failed. Try plugging it into a different wall outlet. If the light still won't come on when you set the handle on it, the base is probably dead and you'll need to order a new charger.
Heads Up
Don't try to pry the metal nub out of the handle—it's not meant to be removed. Just clean the surface.