As soon as you turn the key to the ON position, is there a clicking those for the fuel pump priming when the check engine light turns on and then off? If doesn't then there could be two reasons. The fuel pump isn't getting power by either from the connector or the MAIN RELAY is bad. I had this exact problem 10 years ago (sometimes the car would start and sometimes it just cranks and won't turn on). I changed the MAIN RELAY (bought at a local auto store) and it permanently fix the problem since then. I read on the internet that a handful of old Honda's have this problem because the the car's vibration/bumps throughout the years would slowly crack the solder off in the main relay; that's a possibility.