What he said. But more. Look into the possibility that part of the equipment that came with your GPS is defective. This could be inside of the GPS box, but first (you have a multimeter or continuity tester, right?) check the plug end that goes into the lighter, the plug end going into the GPS box, and the connection between them.
The question to ask is, what is different? You know the lighter works. Have you checked the GPS cord in the Camry recently?
Lighter =|>-----------------<|= GPS