My 97 civic has been running fine up until today. I started my car and while I was letting it warm up, (about 5 minutes approximately) it died. So I started it up again and it ran fine. As I was backing up down the driveway to leave somewhere, I got to the stoplight by my house and just as I slowed down for the red light it died again. I pulled off the spark plug wire and tried to test it for a spark and I got nothing. I pulled the ignition coil and had it tested and it tested OK and I replaced the ICM. After trying replacing those two things it still did not start. I decided that the whole distributor was toast. Is this an accurate assumption, or am I missing something?

Perform tests in Sections A and B below, before doing anything else:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-46563.html

Does the CEL come on and go off normally? Have you ever replaced or resoldered the main relay? If the CEL is okay, replacing the distributor housing would be the next step, if you are absolutely certain the coil is good. I recommend going with a genuine Honda housing, in this case, since we have had many problems with aftermarket distributors.

Personally, I would replace the coil and main relay, due to the age of your Civic. I have seen a number of coils that bench tested okay that were bad.

Be sure to test all under-dash fuses, particularly the ACG (S) (ALT) fuse, with a test light or multimeter:

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

This may be Fuse No. 24. Do this carefully or you can waste a lot of time and money later.