sometimes won't start, but runs fine... on 1997 Honda Civic

Every now and then my car won't start. The battery is new, the engine turns over and over by the starter, but just doesn't fire. The weird thing is, when it does start (eventually), it works fine - no sputtering, no stalling, no problems. A mechanic told me the fuel pump was probably buggered, but I would have thought that, if that were the case, it would cause problems AFTER it started also?? What could cause this isolated problem of starting that doesn't otherwise affect the engine running? Please help!!

Asked by for the 1997 Honda Civic
In most cases the fuel pump relay is the culprit. There are other things that could cause this but usually the first thing I do when a customer brings their Honda in with a complaint like this is to replace the relay and have them take the car to see if the problem goes away. It fixes the problem about 90% of the time and the relay is fairly reasonable in cost. The relay is called the PGMFI main relay.