I haven't checked my FI Main Relay but after reading in this forum I figured out that the main relay issues happens because of over heating, My accord would crank fine but would not start sometime and lately I have seen this happening more often in the mornings when the outside temperature is 30 degrees. So at that outside temperature and first time trying to start there is no way the relay can be hot so that is why I am guessing it might not be relay.
Do you still recommend to change the FI Main Relay just because its too old? I will highly appreciate your suggestions.

If the Check Engine Light comes on for 2 seconds and then goes out, when the ignition switch is turned to ON (Position II), then the problem is distributor related. Replacing the Ignition Control Module (ICM) and coil usually solves the problem. If the distributor cap and rotor have not been replaced in 60,000 miles, now is the ideal time to replace them. I doubt that the main relay has anything to do with your problem.