Saturn SC2 starting issue

I have had a problem with my car not starting randomly for over a year. Two different times, months apart, I would go out to my car and it wouldnt start. Both times, I would send it to the shop, and they would tell me it started right up. They mentioned it being flooded with fuel. Now the car is having problems on a daily basis. Sometimes it will start; more often, it will either not even turn over; or it will turn over very slowly, sometimes after numerous attempts. A couple weeks ago, I could drive it to work, and then drive it home after my shift after it had sat for 8 hours. But if I would go to different stores and shut it off more than once or twice, it wouldnt start up again. Usually in those situations, it wont start for hours or even days, but ill come back and try 3 days later and it will start right up. The battery is new; the starter, alternator, and coil packs have all been tested/or replaced; battery cables are new. The car was running hot, which I thought may have caused it to not start, but I replaced the thermostat which fixed the overheating, and there are still starting issues. Wont turn over. Dash lights, radio, running lights all come on. But when I turn the key to attempt to turn it over, the running light shut off. It has also clicked before when I would try to turn it over, but it no longer does that. I do hear a click noise when I turn it over that sounds like it is coming from inside the cab, down under the glove compartment. I dont know what it is, but that is the only noise it makes. In a day or two the car will probably start. And if I run a couple errands to a few stores, it probably will not start at the 2nd or 3rd stop. I would rather not throw money at the ignition unless I can be sure thats what it is and not something simpler.