I also had intermittent starting problems with my 94 Accord EX automatic. Eventually it didn't start at all an ended up replacing the fuel filter (about time after 200k) but this was not the problem. Considered the possibility of it being the fuel pump, but with the key in the ignition turned to the first click before starter, could hear the fuel pump running.

Symptoms: Could turn the key on and engine would crank, but no dash lights. A Honda mechanic said that it was the ignition module (not ignition switch) in the steering column. Changed it out and that fixed it.