My Expedition would not start. The battery was fully charged. We tapped the starter, thinking the brushes may have hit a dead spot. There was no "click" when we turned the ignition on. Two days later, before purchasing a new starter, I turned the ignition key and it started. I'm thinking it may be the solenoid. Also, the turn signals don't work when the steering wheel is all the way down. Could there be a short in the ignition wiring? I'm thinking there's a short in the turn signals.

 

You might have two separate problems .
If the turn signals don't work with the steering wheel positioned all the way down there may be an open circuit in the wiring from the switch to the flasher.
There is a path the circuit has to follow in order to activate the starter assy. Some of the items in the path are the ignition switch , trans range switch,primary solenoid , and then the starter relay. A good place to start checking is right from the battery terminals . The path includes all the ground terminals and the positive side wiring from the battery to the junctions and the fuse panels. You may just find one of them in need of some attention like cleaning the connections. Many times this type partial connection will act up after the temp drops.