OK, I can't tell you anything about the problems you are having with your car, but I would greatly apperciate it if you could let me know the story when you figure it out cause my car is starting the same way yours is and my ac is doing that too. I might have done something about the AC, but I have no idea how it would tie in. Whenever I had my headlights, radio, amp, subs, radar detctor, and all the other normal junk on, the AC was horrible. When I turned the radio, amp, and headlights off, everything worked fine. I had also been having problems with shutting the car off and then not havng enough power 1 min later to start it again. I cleaned the connection on the battery, and it hasn't really given me any ac or power problems anymore. That starter however, is not at all as bad as it was. but she still acts up about 1 time a week. I know it sounds a little nutty, but go figure.
Give it a try. Sorry it's so long, I'm just getting used to this.
Lata, Mike