Have starting problems very similar to what several others have described: Car which has been very reliable in starting for over a decade, always will crank but INFREQUENTLY will not start or will die immediately and not start again sometimes for 1/2 hr; then it starts. Engine lights behave as normal. Both local mechanic and then Honda Service see same behavior. Several components replaced in fuel and ignition systems, but overall problem remains the same. When double checked by local Honda service, with consultation with Honda service "Central," mechanic indicates it likely is the computer, requiring ~ $1100K to replace. Problems began in cooler weather, and car has not been hot whenever the problems occurred. No stalling while being driven. Any suggestions welcome, but I need to be able to take it to knowledgeable person/shop in Fort Worth/Arlington.
Thanks in advance...

Does the Check Engine Light come on for 2 seconds and then go out, when the ignition switch is turned to ON (Position II)?

The Check Engine light and others come on for ~2 seconds, then go out. However, this is when engine starts, which is ~90% of the time. I'll watch closely to see what happens the next time the car doesn't start.

Have now attempted to start the car about half a dozen times over the period of 24 hours. Twice it started right up and 4-4 times it started but only after a good deal of hesitation/rough running. In all cases, the Check Engine light came on when the key was put to position II and then went off in 2-3 seconds.

To this point, it has not failed to start for me since bringing it back from the Honda place, so I cannot say that the Check Engine light behaves differently when there is no start. One of the mechanics told me they had started the car perhaps dozens of times without fail, and then it would not start until left for ~ half an hour; then it started.

Any ideas?

Above should read Twice it sarted right up and 3-4 times it sarted but only after a good deal of hesitation/rough running.

The problem is with the distributor. Replacing the Ignition Control Module (ICM) and coil should solve the problem. Be sure to apply silicone heat transfer compound to the back of the new ICM; otherwise, it will not last long.