Why won't my 92 Honda CB750 start?

Hi, I have a 1992 Nighthawk (Honda CB750), that clicks at the starter solenoid instead of actuating the starter motor. It's been sitting for about four months while I tried to fix it, gas tank and carbs drained. I've tried (not in order):

-Replacing the Starter Solenoid and Main fuse (twice, the second time, it had gotten water in it…)
-Replacing the Starter Motor.
-Charging, then replacing the battery (I've checked it before trying to start it, it usually sits just over 14v)
-Removing, cleaning and rebuilding the carbs
-Replacing the battery cables
-Drained the gas and carbs and filled with new gas

Maybe there's a clog in the crankshaft casing or a short in the cables… I don't know, and I'm really in need of advice. Any ideas?

You never mention the starter button

So with the ignition on, run a direct wire from the battery to the starter, bypassing everything.
make sure it is a fat wire at least a 10 gauge
If the motor turns then the problem is a fuse, or a relay, or a fuseable link
If nothing then pull the starter motor and try again after you make sure your engine turns over and isn't seized
Oh yea- Neutral is switched as well as engaged clutch

The clicking has NOTHING TO DO WITH THE CARBS. It is probably the starter, starter selinoid, or the battery is junk

check to see if the horn and lights work. If so then the battery is good, so it is one of the other two listed above.

Is starter being allowed to turn? Not jammed against flywheel etc?
have we tried jumping power directly to starter and by passing wiring? If this works. Then we have a voltage drop or too high a resistance between battery and starter.

Broken!