1996 Saturn Car Won't Start

I am new on here, but not new to cars. Except for a Saturn.
My problem is that my car will not start. I have had this car for 2-3 weeks now. Never had a problem starting. The only real problems I have had is that when I shift into another gear, the idle would go up, then calm down. Tuesday, I drove 30 miles to an appointment, I shut the car off, and came back out to start it and I had nothing. The battery is good, the light panel was lite up, but when I turned the key, nothing. It won't even click. It acts as if the battery is dead, but I changed the battery, just in case. Still nothing. Before this happened, there were times when I would try to start it and would have to hold the gas pedle to the floor, then it started. I have just a few thoughts on the problem, but not real sure. 1. Ignition control module, bad starter, but when I try to roll start still nothing. I have checked and rechecked fuses, all good. Anyone have a suggestion as to what my problem is? I have another for parts, but it is automatic. This one I am having problem with is a 96 1.9 mfi, standard.I can't perform any test because it won't even crank over