Standard shift. Car began to be harder to start as the weather got colder until all it does is click behind the glove box and refuses to crank at all. Replaced main relay without change. Checked fuses. Looks like all good. I don't hear fuel pump but it won't crank so pump issue is moot. Analyzer says no codes in ECU. Battery shows full on 2 different chargers. Connections tight and clean. Can't get under vehicle to jump across starter due to ice on ground. Haven't tried push start. This Honda does not use electronic key. The key is of a type that has no transponder, one of the reasons I bought the vehicle. As far as I can tell, there is no immobilizer. There is no other security on the car. I have only one key and it only unlocks the driver side door, which also sux. There is no indication that anyone has modified this car in any way. It has 270,000 miles.
Since the battery reads good and yet you're still hearing clicking noises when you turn the key, the next logical thing which could be bad is the starter. If the solenoid has gone out, you might hear a relay click, but there'd be no starter action. To test this theory, you'd need to take the starter out and have it tested.