What could be the reason car won't start?

I have a 1999 Saturn sl1, having a starting issue. All lights and dings work in the car, it starts when it feels like it. when it doesn't start it just doesn't turn over at all. Battery/stater and alternator are fine. You can change the starter relay switch which is what I did thought that might be the problem but it didn't start yesterday when I drove it to the grocery store. but went the next morning and it started right up. it may need a thermostat issue, im not sure but will keep you inform

Next step is check the starter motor!

Did you check battery, starter, fuzes

I have a 94 SL1, am having the very same types of issues. I believe it is due to the ignition cylinder. Haven't had this car for even two weeks yet, and still paying for repairs. I was able to drive the car without a key in the ignition, also, the key can also be removed from any position which will leave the car in an "on" position; therefore draining the battery. I was hoping to read at least someone else had found that to be a he issue. Only paid $700 for the car, but drove it two blocks home and had it towed to have the clutch cable replaced, plus new wipers. That bill totaled $435.00. I'm on disability, having my seventh brain surgery this Thursday and my four year old pup, Buddy, is blind. I cant keep putting g money I to this car, hoping its the last repair. I will follow up with the results, whether it fi that s it or not so others benefit. What I have read was somewhat helpful.