If you look at ecu, it has four pins instead of five. That missing circuit was the other half of the ballast. Its now in the ecu.
If there is power, ground and ecu is grounded and assumed good and pickup is good there is no reason it shouldnt run.
Are you talking about the pickup coil in the distributor? Is that something that can be bad and only fail when car is warm and has run for a while. The restarting the car when hot and having no spark has been a solid symptom for a while.