93 Geo Storm starts, then won't start

It could be the advance system in the distributor. When the engine is running, check the timing, see if it fluctuates. Accelerate the engine and see if the timing advances.
You said it "just doesn't wanna turn over anymore." Do you mean start, or crank? If you mean crank, check the battery. Make sure it is fully charged, and while at the parts store, have them perform a load test to see if it holds a charge.
Does the engine refuse to start when cold or hot?

Pull the cap and crank the engine while watching the rotor to see if it turns. Can you turn the rotor by hand? Look at the underside of the distributor cap to look for wear.
"It refuses to start when its hot only. " So it will start when cold? If so, spray some carburetor cleaner around the vacuum lines, fittings and wear the intake manifold mates to the cylinder head with the engine running. Listen for the engine reving or smoothing while you spray. Or, do you mean when the weather is warm?

A rusty distributor definitely isn't helping anything. Try testing the fuel pressure. Make sure it's around 30 PSI. If the engine starts when cold but not when hot, it could be vapor lock caused by insufficient fuel pressure.

1st diagram is for Single Overhead Cam Engine, 2nd is for Dual Overhead.
The fact that the rotor turns when cranking but not by hand is good. It means the distributor shaft isn't snapped.
Borrow a fuel pressure tester from a parts store and check the fuel pressure. When cranking, can you hear the injectors clicking, indicating they're opening and closing?