I am actually going through this in my 95. It's a stock auto car.
I haven't really diagnosed what the hell it could be, but I need to drive my car so I'm going to start diagnosing it.
Download the FSM from here.
Go to 240sx, click your year, click each section and then download it.
Right off the top of my head I would say
-Check your grounds ( battery positive, battery negative to chassis ground, negative to engine block, etc)
-Check all your connectors. Could be a loose connection, or corroded, or that the crimp has failed and the wire is barely making any contact.
-Ignition switch? S14s are 25-28 years old at this point. Could just be a crappy switch.
-Electronics: could be a starter relay, fuse or ANYTHING in the starting circuit. I'm downloading the FSM now and I'll take a look to see what exactly goes on in the circuit.
As far as the problems I had with my car.
1. I'd be driving and it would randomly start stuttering and die. It would not restart, no click or anything. I turned the key and it did nothing.
By the time the tow truck would show up, it would magically start.
I fixed it by throwing parts at it. I did a new fuel pump, fuel filter (in engine bay), MAF, knock sensor, new distributor and rotor.
That problem went away.
2. I still had the no start issue. I could wake up, drive to work, park the car for the entire day at work, and when it was time to go home it would not start.
It would do that at THE MOST inconvenient times. Quite a few times I had to work late and when it's 7:30-8pm it would do nothing.
Then it would randomly start when the person who is picking me up is like pulling into the parking lot.
So this is considered a no crank on a cold start. As in the car does not crank when the engine is cold.
A no hot start is when you drive to get groceries or even stop at a gas station for a few minutes, the engine will not start.
I don't remember if I always got cabin electrical power or not. I do recall the gauge being lit so I would assume so.
If the ONLY thing you did was jiggle the battery cable a little, then I would definitely suspect that cable.
Get your hands on a multimeter. Disconnect the battery and remove it from the vehicle.
Measure the resistance from the end of the cable to wherever it goes to the fusebox & starter.
It should be almost 0 ohms.
I'd suspect you have enough corrosion on the terminal that it's getting a crapload of resistance from it and not allowing any electricity to pass through.
Here's another thread from way back in the day,
www.240sxforums.com
Let me know what you find.
I haven't really diagnosed what the hell it could be, but I need to drive my car so I'm going to start diagnosing it.
Download the FSM from here.
Go to 240sx, click your year, click each section and then download it.
Right off the top of my head I would say
-Check your grounds ( battery positive, battery negative to chassis ground, negative to engine block, etc)
-Check all your connectors. Could be a loose connection, or corroded, or that the crimp has failed and the wire is barely making any contact.
-Ignition switch? S14s are 25-28 years old at this point. Could just be a crappy switch.
-Electronics: could be a starter relay, fuse or ANYTHING in the starting circuit. I'm downloading the FSM now and I'll take a look to see what exactly goes on in the circuit.
As far as the problems I had with my car.
1. I'd be driving and it would randomly start stuttering and die. It would not restart, no click or anything. I turned the key and it did nothing.
By the time the tow truck would show up, it would magically start.
I fixed it by throwing parts at it. I did a new fuel pump, fuel filter (in engine bay), MAF, knock sensor, new distributor and rotor.
That problem went away.
2. I still had the no start issue. I could wake up, drive to work, park the car for the entire day at work, and when it was time to go home it would not start.
It would do that at THE MOST inconvenient times. Quite a few times I had to work late and when it's 7:30-8pm it would do nothing.
Then it would randomly start when the person who is picking me up is like pulling into the parking lot.
So this is considered a no crank on a cold start. As in the car does not crank when the engine is cold.
A no hot start is when you drive to get groceries or even stop at a gas station for a few minutes, the engine will not start.
I don't remember if I always got cabin electrical power or not. I do recall the gauge being lit so I would assume so.
If the ONLY thing you did was jiggle the battery cable a little, then I would definitely suspect that cable.
Get your hands on a multimeter. Disconnect the battery and remove it from the vehicle.
Measure the resistance from the end of the cable to wherever it goes to the fusebox & starter.
It should be almost 0 ohms.
I'd suspect you have enough corrosion on the terminal that it's getting a crapload of resistance from it and not allowing any electricity to pass through.
Here's another thread from way back in the day,

If It's Not The Starter Or Battery...
OK, 89 240SX KA24E W/ M/T - PROBLEM: WON'T START, JUST CLICKS. WILL PUSH START FINE. I KNOW ALOT OF PEEPS HAVE ASKED ABOUT THIS IN OTHER POSTS, BUT THE REPLYS ALL SUGGEST WHAT I'VE ALREADY TRIED. BATTERY - GOOD(FULLY CHARGED AND TESTED) STARTER - REPLACED WITH TESTED STARTER THAT SPINS LIKE A...
Let me know what you find.