Ok, so I've been reading about starting issues concerning Honda's and have a few things similar to what i have happening here.

When you turn the key to accessories, all dash lights come on as does the fuel pump, but when you turn one click past to engage the starter, I get nothing.

This happened last night, so I push started it, and it started just fine. Then the started worked as it should. Then I drive into work today, and it is doing the same thing.

I read where a bad Main Relay could do this, but that would also make the fuel pump not work. Since I am getting power to the fuel pump, I don't think this is the problem. Also there was another post somwhere that mentioned that the ICM could be bad if you get the engine to turn over, but there is no spark.

I replaced the ICM a couple of weeks ago and it seemed to be working just fine until last night.

Is there anything else that would make the starter only work intermittently like this?

 

"no crank" will not be caused by main relay trouble.
first check Battery connections and grounds.
Then check that the ignition switch is putting power out to the small solenoid connection on the starter.
Any alarm systems that might be causing the problem?