Find the fuse(s). Replace the bad one(s).
Lights and ignition go through fuses. If your charger says your battery is charged, it probably is. Check the lighter guage red wire(s) from the battery. They should go to a fuse. The heavy wire should go to the solenoid, and that might be where the other feed wires tap from. If you don't have lights, it probably isn't a safety switch malfunction (at least I think my lights come on w/o the engine running, when they're installed.).
Jim