1993 honda accord ex has trouble starting when cold, starts fine when warm.

the car has had this problem since i got it earlier this year in February. the car will crank but will not start when it has been outside in cold weather for a while (mostly overnight). it is not the battery, i had autozone test it. there have been times when i would put it on a overnight charge and spent 30 minutes to an hour cranking it, sometimes it will start after an hour of constant cranking. but when it warmed up it was good, except a few times on nights when a bad cold front has come through. now it is getting cold again and it is having trouble. as of right now the car will start up fine, today was a warm today and luckily it started. i forgot to mention, when it does start it will start right up the rest of the day, granted it is not really cold and has not been sitting for a while. it actually does not have to get that cold for this problem to occur, if it even gets in the low 50s overnight this will happen. earlier this year when it was cold it would be fine and start up the next day if it was parked in a garage. well that is not a option now. i really want to figure out and fix the problem before, well, there is no more warm days. the past couple weeks i have been researching and i found that condensation may get in the distributor cap overnight which may be causing this problem, but i took the cap off and there is no condensation on the cap? i tried wiping it off with a towel and that didn't seem to work. the main relay is good, i can hear the fuel pump turning on. and this distributor has to be good since i drove it today? any help would be appreciated.