Make sure you have a 12V source to your ignition system during cranking. The way I did mine the first time I only had power in the run position. When I did the initial setup I was using a remote switch and had the key to run so it was fine. After that it would start ok the rest of the day. The next day it was very hard to start but it finally did. Mine was just the way I wired it but I could imagine that it would be possible to have a bad ignition switch causing the same problem. I would not have thought it would start at all the way I had it but a warm engine must have enough spin left in it when I released the key that it would fire. I imagine its all in the timing that you let go of the key.
May not be your problem but its easy to check and eliminate as a possible cause.
Most of the time a bad pickup will show with an ohm meter and more often than not its the wires that are bad. Make sure while you are testing you flex the wires and operate the vac advance to make sure there is not a break there. Also make sure you have the polarity correct on the pickup to module wires, you would be amazed how well it runs out of phase untill you get it in phase and see the differnce. If you are using a ford module its just purple-purple and orange-orange. The ford modules also have a start and run mode, seems like I read somewhere that they are differnt transistors so it is possible to have one mode fail and the other one still work. I think I read that that is the white wire going to the module but Im not sure. I am told that most of the time it works without the start mode hooked up because all that does is a 10 retard for easier starts.
What year are we talking about? Is there a Thermal Vac Switch on the advance line to the dizzy? That could explain a differnce betoween hot and cold starts if the pickup coil wires are bad. Modules are known to be sensitive to temp and voltage, can you see any pattern to temp or voltage when this happens?
Good Luck!
