I have a 94 Honda Civic DX. Last summer it became almost impossible to start in hot afternoon weather but the next morning (cooler) it would turn over without a problem. I did some research and found that it was most likely the Main Relay. I replaced it with a new Main Relay and the starting problem went away... for a while.

Seven months later the hard starting returned but it was now hard to start even in mornings and cooler weather. It also seemed to be most difficult after rainy or very damp weather. I would crank the car and the Check Engine Light would come on, stay on, and the car would not start (I did not hear the Fuel Pump power up after a couple of seconds like I had before). Now, here's where it gets strange, if I left the key in the ignition and turned to the second click, the Check Engine Light stays lite for about 2 to 3 minutes (not seconds) and then it goes off and THEN the Fuel Pump powers up (I hear it).

What is keeping the CEL on for those 2 to 3 minutes and delaying the application of power to the Fuel Pump until then. Its quite repeatable as long as the car is off for about 30 minutes between attempts. The Fuel Pump will power right back up if the car is turned off and then turned back on only a few minutes later.

 

Main relay again maybe? You have all the symptoms of a flakey main relay. Unbolt the relay and let it hang by the wires so you can reach it. Next time it won't start, tap on the relay and see if that revives it.