Hello,
I have read through many of the postings on same topic, but would like to add details of my situation. My 95 Civic EX has run perfectly for 125k miles. When I parked it yesterday, would not start couple of hours later.
The CEL goes off after 2 seconds, I can hear the fuel pump make slightly audible noise after that. My friend hooked up tester and got a 5.2v reading on the MAP sensor, he replaced the ICM following instructions from TXgreasemonkey (thank you), but still just cranks. Oil light goes out while I'm cranking.
I will add that I've read some about ambient temperatures causing problem with main relay, and also that the ECM rarely go bad on Hondas.
Also, I don't believe we are getting a spark, as my friend took off coil wire while I cranked and did not see spark. Decided to buy whole coil assembly which evidently contains it's the ICM as part of it, but did not yet install it as was looking for any confirmations that that might indeed be the solution. I can' take the individual ICM back to store once it's been installed. Hopefully some expert can give me good pointers, as I'm not mechanically inclined enough to figure this out myself while trying to avoid getting ripped off by a shop.

Your problem is distributor-related. The ICM and coil are separate components. I would definitely install the new coil, since you have already installed the new ICM. Ensure your buddy applied a thin, even coat of silicone heat-transfer compound to the back of the new ICM. I normally recommend installing new ICMs and coils at the same time. From experience, I recommend proactively replacing ICMs and coils every 120,000 miles or 10 years, whichever comes first. This will likely solve your problem. If you install the new coil, you should have your car running in 10 minutes. Be sure to disconnect the negative battery cable, prior to working on the distributor. Ensure connectors are clean and tight. If for some reason the car still doesn't start, check all underdash and underhood fuses with a test light or multimeter:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post252145

P.S. You never want to remove an ignition wire from the distributor to check for spark. Instead, disconnect the spark plug wire from the spark plug, ground an old plug, and check for spark. If you remove an ignition wire from the distributor to check for spark, you can over-stress and ruin the coil in no time.

Your problem is distributor-related. The ICM and coil are separate components. I would definitely go ahead and install the new coil, since you have already installed the new ICM. Ensure your buddy applied a thin, even coat of silicone heat-transfer compound to the back of the new ICM. I normally recommend installing new ICMs and coils at the same time. From experience, I recommend proactively replacing ICMs and coils every 120,000 miles or 10 years, whichever comes first. This will likely solve your problem. If you install the new coil, you should have your car running in 10 minutes. Be sure to disconnect the negative battery cable, prior to working on the distributor. Ensure connectors are clean and tight. If for some reason the car still doesn't start, check all underdash and underhood fuses with a test light or multimeter:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post252145

P.S. You never want to remove an ignition wire from the distributor to check for spark. Instead, disconnect the spark plug wire from the spark plug, ground an old plug, and check for spark. If you remove an ignition wire from the distributor to check for spark, you can over-stress and ruin the coil in no time.

Proceeded to install the distributor/coil assembly and car now running fine. Thank you for your prompt response and also for the FAQ you wrote -- impressive!

Good job and thanks for the update.