If you replaced the distributor, and did not place index marks on the distributor and mounting bracket, then the timing is likely way off. Most shade tree mechanics end up retarding the timing too much. Follow my previous instructions on how to advance the timing, after placing index marks on the distributor and mounting bracket. The engine should start, if you do this. If you didn't apply the silicone heat transfer compound to the back of the new ICM, however, you may have ruined it. I can set the timing on most Honda's of your vintage very close by ear.

Failure to replace the rotor and distributor cap every 60,000 can cause high resistance in the secondary, resulting in high voltage discharging through the ICM or coil. Electricity will take the easiest path to ground. This is how many ICMs and coils are destroyed on Hondas, even if they are new components.

Their were problems with the Honda Ignition Switch around that year. Seen so often I would almost bet on it.
Go to The12vol.com, select Vehicle wiring, year and model, it will tell you the color of the Bat+ wire, Ignition wire, and Start wire, Test at Ignition switch, Little plastic cover will need to be removed, good luck.