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I have a recently acquired '86 vet that I still have on jack stands replacing the clutch M/C & S/C. Engine starts good, and will re start after it it shut off. After several minutes, the engine will not turn over.
At that time, if the battery is disconnected and reconnected, it will start without any problem.
If you mean that there is no power to the starter it sounds like a problem with the VATS system.
You could start by measuring the resistance of the chip in the key, open the connector comming out of the bottom of the steering column and insert a 1/4 Watt resistor of similar resistance. If contact with the chip is intermittant, the car should then start every time. In which case you can leave the jumper in place or replace the key.