Chrysler Repair: PT Cruiser wont start, flashers, passenger seat

Question
I have an '02 PT Cruiser, there all the same engine I think 4 cyl.  The other night my wife was driving I was in the passenger seat, and the car just quit, we were on the freeway at the time, she pulled over to the shoulder and we put the flashers on.  The car wouldn't start.  It was about midnight and I tried to start the car myself, but I'm not sure if it was turning over or not?  Called AAA, they came and towed the car home.  In the morning I tried to start the car and it definitely wasn't turning over, I did hear the clicking sound around the battery area, I assume its the relay.  I'd assume it's the starter, but I've never had a problem with it before, also it started right up the other night, and if the starter was bad it wouldn't explain why it just died on the freeway?  I did take the battery out and took it to a shop near by, and they charged it and tested it and said it was basically good about 80% they said, but that it probably wasn't the problem, when I reinstalled the battery, I had strong lights, but car still didn't turn over?  Any help would be appreciated.

Answer
the starter does one thing and one thing only  start the engine moving   it has nothing to do with it while driving.  U messed up by taking the battery out because u erased any codes that were in the computer system that would aid u in figuring out what the prob is.