I wouldn't start replacing things, you will end wasting a lot of money replacing parts that could very well go for another 100k. put the effort into properly diagnosing the problem.

My guess is that it is your PGM-FI relay. It is a common problem for older civics.

What you need to do is turn everything off and roll up the windows so you can hear the car real well. when you first turn the key the CEL will light up and you will hear a click, the fuel pump runs for a second and then another click and the pump and CEL turn off. If this doesn't happen when the car won't start but does when the car will start, that is your problem.

There are plenty of threads on how to fix the relay if you search.
or http://www.tegger.com/hondafaq/mainrelay.html