98 Civic LX – Cronk/No Start & will not shift out of park.

i have a 98 civic LX automatic. While driving occasionally the rpms drop to zero and car wont start for about 5 minutes. The engine will crank, but it will not start. The brake pedal will activate the brake lights, bit it will not activate the shift lock solenoid. During this time, the engine will crank but not start. After 5-10 minutes, the break pedal will start activating the shift lock solenoid and the car will start. While the car will not start, I tested the distributor and found both the Ignition Control Module and the Ignition Coil were getting power, but the Ignition Coil was not firing. I replaced the coil and the car started fine. While test driving, the car died again and it was stuck in park. Looking for any ideas?

I also have a transmission problem, but I believe it is unrelated. The transmission will go into a sort of false neutral after heavy driving (fast hwy speed or hills) After shifting the car into park and waiting for a period of time, it will start driving again. I have checked the two small screens in the shift solenoid, but they are clean. The transmission fluid has always been full synthetic Honda approved, and it is full.

Recent service included:
Timing belt change
New Distributor Cap and Wires
New Spark Plugs
Valve cover Gasket
Transmission oil change