On the Honda LX Forum on page 5 I found this...
Originally Posted by phootbag
Possible electrical connection, ignition coil, ignition control module ( igniter ), ignition switch, PGM-FI main relay.
Does the engine crank during the no-start or does nothing happen at all? Does the check engine light come on and go out when turning the key to the ON position? If/when the check engine light goes out during the no-start condition, can you hear a moderately loud 'click' from behind the drivers dash? When the no-start occurs is there spark at the spark plugs?
that Part where you say. "If/when the check engine light goes out during the no-start condition, can you hear a moderately loud 'click' from behind the drivers dash?" I have that problem... in my 91 Accord... I've changed the ignition switch... a few relays... and still it does nothing when I turn the key... I know the batt and the starter is good cause I can get it to turn when I hot wire it. Help me if you can.