2000 SL1 wont start, or turn over
 

My Saturn has about 160k miles on it. It was driving fine the other day until i stopped at a store. I went back out and the car would not crank. All electronics were fully functional, including the headlights. And when we would turn the key, the lights would not dim. This made me think that it was not the starter or the battery. When we turn the key we get NOTHING. No sound, no clicks, nothing. We parked the car and came back about 5 hours later and it cranked on the first go. I drove it home, cut it off, and attempted to restart it, and was unable. I left and came back about 4 hours later and it started twice. I thought maybe something was over heating. I got up the next morning and the car would not start again. I have not attempted since. Any thoughts, or help would be most appreciated.

sounds like weak battery or loose/corroded battery cable or starter solenoid. I know you said electronics worked fine with key in, but that does not guarantee battery has enough juice to get the starter to turn the engine. If battery no longer holding a charge, would behave as you described (time delay between starts may have been giving it just enough time to recover for the next start).

Starter solenoid may also be defective, giving you the silence when not turning over (its not engaging the starter) and the failure to crank the engine when warm (hard to tell since your description only indicated you could not restart it after driving -- whether or not it cranked at this point was not included -- I assumed it did not crank -- if it did, back to weak battery)

Your Saturn is 10 years old and high mileage. There frankly could be a number of reasons for this symptom but the conclusion you drew is it is not the starter, based on your description is probably wrong.
Why wouldn't be the starter? Nothing happened
No lights dimmed, no funny klicky noises as the starter tried to work. It just sat there.
Certainly if the starter did not work, it is highly probable that what you are seeing would happen exactly as described.
It is an electric motor, if the brushes get so worn that operation is iffy than what you are describing certainly is a possibility.
Of course so or are other things too. But with the miles and the years, a starter is a good bet.