Wow, a 1939 Plymouth convertible, welcome to the forum. Now, please don't get upset with me. While you haven't mentioned your background, I assume you have mechanical experience as you mentioned having rebuilt the carburetor.. If the car started after replacing the battery, and not since the work you've summarized,I would think you should still see spark at number 1 cylinder...this is the part that I hesitate to mention - the point gap in the distributor must be set at least approximately correct and the points must both close then open to obtain spark..again, forgive me if I've insulted you