Classic/Antique Car Repair: 1965 T-Bird First Start -up after sitting a few days ., stock distributor, stock coil

Question
I have a 1965 T-bird with ALL NEW ENGINE, TRANS, AND every moving part from the block up. All genuine parts w/AC. We put an electronic distributor in place of the points.
Once the engine catches and runs, it's like a kitten. Smooth healthy sounding and starts RIGHT BACK UP if shut off.
Now We have tried ether, poured gas directly into carb, checked the ELECTRIC CHOKE. My friend has the same BIRD with no start up problems.
Here is the ONLY THING I CAN THINK OF: I have a battery terminal SHUT-OFF disconnect on the post of the battery. Could turning off the battery power effect any of the electronic distributors condensers or coil STORED POWER in them. One time I went to start the bird after 3 days and on the FIRST key BUMP it fired right up, and I don't remember if I turned the battery off prior to that day. I can fix or repair all my toys, but this one has me scratching my head big time. THANK YOU for ANYTHING that will put light on this problem.

Steve

Answer
To better understand this problem let me ask a question or two. First what kind of electronic ignition did you install? is it one of the aftermarket units that installs inside the stock distributor and uses the stock coil? If so the brand and part number if you can supply that. Or did you put in a later model Ford electronic distributor and control box? If so what year car did it come from? Let me know and then I think I can figure it out.
Brad