Sounds like a fuse, since the cig lighter and radio constant are often on the same one.

Fuse might be called cig ligt, radio, or something like that. If you have a manual for the car, it usually lists all things powered by each fuse. Worst case, you'll need to check them all. This fuse is probably 20 amps...15 minimum, so you can narrow down your choices.

Toby