I own a 93 saturn sc1. My car generally doesn't start. I turn the key and it starts to turn then rolls back and doesn't start. After a couple turns, doesn't even do that. I can jump it. But even after running it for a good 30 minutes or better. No luck. Doesn't turn. Brand new battery and the alternator came back okay after a quick check at advance auto. Starter maybe? The car over-heats and we're thinking it might be related to the electrical problem. Like the fan maybe not getting enough juice, as the overheating isn't as bad on the highway. Any thoughts? This is making me crazy! D:

 

change ects and connector. It has likely failed and is sending bogus data to the PCM about engine coolant temp. This, in turn, will keep the PCM from ever turning on the fan as it thinks the temp is much lower than it really is.

To make matters worse, the ects also controls air/fuel mix. When it fails, it almost always makes the fuel mix way too rich, which in turn can make it really hard and in some cases impossible to start the engine.

Use replacement brass tipped ECTS (2 wire device--not the single wire device - your car has two temp sensors) and connector sourced from a GM dealer.
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As for the non-cranking problem, check that the battery meets or exceeds CCA specs. Could be marginal cell in battery. Yes it happens with new batteries too.
I would take the car to advance auto and have them check the fully assembled charging system just to be safe.

Also check all battery cables for tightness and corrosion and check the electrical connections at the starter.

Barring any issues there, I'd pull the starter and have it tested before you blow money on a new one. Does sound like a dying starter to me though.

 

Dealer etcs only