WHat Could It Be
 

I have 98 galant with 140,000 miles. I drove to th store about 3 city blocks with my air conditioner on. The car drove just fine nothing out of the ordinary. I came out of the store after about 10 min. and when I went to start the car it would not start. I had all dash lights, radio, power. When i turned the key in the ignition it would not turn over. It was quiet no clicking or nothing. Just dash lights. Someone tried to jump me no luck. I called AAA waited about 40 minutes by the time they got there the car started no problems drove home fine. Skipped a day driving and the following day I drove all day about 25 miles total. I had no starting issues. I did not turn on the air conditioner. I waited until I got close to home to test it out just incase I had any problems. I turned the air on about 2 blocks from home it seem to be driving fine I parked then tried to restart it just to see and I did the same silent no start all lights and power. I just went out to check it and it started fine. What could this be? Would a Oxygen Sensor do this? Or is it something related to the AC? A little information A few weeks ago my heat shield to my CAT came off. HELP

the electrical part of the ignition switch is notorious in that model of galant for failing. same symptoms your describing. also the distributors are known to fail in that version of the 2.4L. usually when the distributor fails it doesnt restart, but stranger things have happened.

I have a 97 that did that same thing usually when I stopped for gas. Long story short the negative battery terminal was just loose enough to fail after it warmed up, I cleaned and tightened both terminals and it never did it again.

Could be the starter going out, just intermittently shows up for now. The a/c just makes things a little hotter under the hood, maybe just enough to knock out the starter until she cools down.