Does the unit work in another vehicle?
If not, the first thing to check is the fuse in the power cord. The adapter (the part that plugs into the lighter socket) has a replaceable 2 amp 3 AG fuse inside it. The end of the adapter, which has the silver tip, unscrews to gain access to the fuse. CAREFUL: Unscrew slowly! The tip contains a spring which may fly out when disassembling. With use, screw cap on plug may loosen. Retighten occasionally.
If the unit works in another vehicle, it could be the lighter socket fuse. Check your vehicle's owner's manual for fuse location and the correct value. If the vehicle is old or the lighter is used often, the socket may be corroded or loose. Replacement of the lighter socket may be necessary.