In looking at the Commander 2000 remote control wiring harness, raw 12v from the 20 amp fuse in the engine is fed to the Power Control switch on the solid RED wire. That switch is not connected to the PTT circuitry except for both getting input 12V from the same source (RED wire) which is available any time the remote control cable is plugged into the engine, and thus allows you to have PTT any time, regardless of power switch position.
Prior to reaching that switch, the RED wire is pigtailed with the center pin of the tilt/trim switch giving you the convenience of running the PTT anytime from any place in the boat that has access to the BLUE, GREEN, and RED wires. Since you said everything works fine in the OFF position, it means that all your PTT components are fine. Interesting problem.
In thinking through this, the PURPLE or RED/PURPLE STRIPE wire is "switched 12v" which occurs when the switch is in the ON, or START positions. As I see it, probably in the control box, some chafing has occurred whereby that wire and the BLUE PTT wires are making contact. Could also be a chafe point somewhere in the routing of the control cable from the engine to the remote control.
Disconnect the remote wiring harness plug in the engine compartment. Looking into the remote harness connector get on PIN 2, the PURPLE (or may be the RED/PURPLE STRIPE......the "switched 12v" line) wire with an Ohm meter and set it to the 200 Ohm or a low Ohmic value with the other lead (clip on an extension wire to get the required distance) and go to the PTT switch in the RC handle and get on the BLUE wire on the back of that switch.
With the switch OFF you should have an open circuit. Switch to the ON position and see if you read continuity. If so, the switched 12v is shorted to the BLUE wire somewhere in the wiring harness or control box (probably since the moving of the control stick moves things around inside the box where the wiring is located and shorts do happen in there. I don't know what else it could be.
Good Luck!