Need help, not sure what to think... Options

[Overkill]

Ok, so here is the situation. I drove to a meeting today. 45 minute drive. I was a tad bit early, so I pulled into a gas station to let some time pass. I let the car run while I waited. I was there for maybe.... 8minutes. I backed out of the parking space, and drove to the meeting. After the meeting, I went back to the same gas station... and got a coke. I turned the engine off while I went inside. I came out, started the car, and moved over to the air pump while I was waiting on someone. I waited for maybe 10minutes while the car was not running. As the person I was waiting for passed, I tried to start the car and all I heard was tick, tick, tick, tick. I thought it could be the battery had died, so I popped the hood. I checked all the wires. No corrosion on the terminals. All the negatives were connected. No loose connections, and the alternator and spark plug wires look good. I waited about another 10 minutes, and decided to try to start the car again... and it started. I felt okay about the situation thinking that nothing major was going on. HOWEVER... as I was driving home on the freeway... my car died. I coasted past a state trooper, pulled over, and put her into park. I turned the key, she started right up. I drove home, backed into the drive way, turned her off, and restarted her.

The spark plugs & wires, cap, rotor, and oil are all new and installed correctly more than 3 months ago. There is nothing wrong with the battery it seems, and the starter would not make the car die while driving. I did recently have a loose alternator belt, but have since tightened it and she has been running fine. I am seriously confused, but would appreciate any help or advice you guys may have.

[VavAlephVav]

once upon a time I had a Neon with some funny issues, It would mysteriously die.
turned out there was a damaged wire along the wirelimb that was beside the motor, somehow it was damaged when a shop did a headgasket replacement.
but It took a long time of intermittent messing up before we finally found it. just had to start unwrapping the wirelimb until we found a bad spot.
but It was blowing a fuse when it did.

may not be the same as your problem, but when you have intermittent problems that just act squirrelly I would suspect wiring or electronics.
electronics will work one minute and not the next, and then work again. anything mechanical will either be broke, or not be broke.
maybe even jiggle the wirelimb in places to see if you can recreate the fault.

when the ecu is suspected the manuals recommend swapping it out to see if that cures it, pretty expensive though to just go buy one, and I think you may need
to have Toyota program it too. that's the way the Neon was.