1999 Honda Passport one click, no crank, intermittent

Only when cold, left overnite. What are most likely faults. Replaced battery and cleaned connections already.

Had the same problem with my 03 Passsat, only happened when air temp bas below 10F. I could jiggle the key, or turn it back and forth and eventually start the car. Replaced the switch (the part that fires the starter solenoid), OK so far.

See if you can jiggle the key and get it to start, or turn the key back and forth… I’m assuming the dash lights all go on?

Does not appear to be the ignition switch or the “Park” position switch. I am suspecting the starter solenoid.

if that “click” you hear is fairly loud and coming from the engine compartment, and not the click of the key itself, then yes, I would suspect the solenoid.

After the voltage goes through all the fuses and switches, it’s tired and weakened by the time it gets to the starter relay. It starts at 12 3/4 volts, in a healthy battery. Each fuse and switch saps some of its oomph. By the time it gets to the starter relay , it may be a shadow of its former, robust, self. It may have fallen to less than ten volts from all of the accumulated resistances.
Your friend, Mr. Voltmeter, can tell you how much resistance is in each fuse and switch. Take the first voltage reading on fuse #16. Record. Have someone hold the ignition key to START (III). Next, read voltage at fuse #20. This is after the ignition switch. Record the voltage. If it’s more than 1/2 volt lower, the ignition switch has excessive resistance.