Classic/Antique Car Repair: 1987 Nissan 300ZX NA, spark plug wires, nissan 300zx

Question
i have owned this car for about 3 years and havent ever had a problem with it as far as engine or driveability. it isnt modified other than just "dress up add-ons." i bought it from someone that completely butchered out the alarm system because it would go off at strange times, so the alarm system is completely gone. having said that they wired the ignition to a starter switch. you have to turn the key to the on position to get power then push the starter button to crank the motor. usually i have to start the car and let it warm-up for about 10 min no matter what the weather is like outside and until it "warms up" it always acts like it is trying to choke itself out. once it is warmed up and driven i dont ever have any problems from it for the rest of the day even if it is turned off and allowed to cool down. it is a standard and most times if i push the gas pedal down to accelerate it will hesitate and shudder but then accelerate. recently i drove it to the store after allowing it to warm-up did what i needed to do cam out of the store and it refused to start. i would turn on the key push the button and it would fire, run for a second to about 2000 rpm and die. it does this repeatedly. i called a friend to bring me some tools. we tested the spark plug wires where they connect to the plugs and i am getting fire there also tested the ports at the distributor and the coil. so we figured and the hayes manual also said it would probably be the fuel pump. we bought a new fuel pump and installed it. we pulled the fuel lines off at the motor and bled the lines reconnected them and tried to start the car. we had the exact same problems and symptoms. i am in the military and i left in oct 07 for training and the car was in the shop at a nissan dealer. they replaced the front and rear engine seals and tested the compression in the cylinders, and also replaced the valve cover seals. they also checked the timing and replaced the timing belt. my father picked the car up for me while i was away and started it about once a week. he did say that it would hesitate but that it drove fine. i did put in an aftermarket stereo and rebuilt several of the wiring harnesses but i have a lot of experience with that and have never had a problem before. none of the harnesses i rebuilt were connected with the motor anyway. i drove this car to where i am currently stationed over memmorial day. the trip was over 1000 miles long but the car did fine all the gauges read in the green and none of the sensors ever went off. this was a sudden problem and i would appreciate any help you could give.

Answer
How are you checking for fire without it running? Just off the starter? Try this...run a wire straight from the pos side of the battery straight to the pos side of the coil and then see if it will stay running long than a second.  BUT, BE AWARE YOU CANNOT KILL THE ENGINE WITH THIS WIRE CONNECTED.  If this works, we will address the hesitation.