Hello all I am new to the forum. I have been researching the Rocket. It will be definitely be my next bike. After reading about Rockey's dilemma, I have decided to register. I have not studied the Rockets electrical schematics yet, so some of what I am saying may not be applicable.
I doubt it is a battery problem. When fully charged a sealed lead acid battery should have about 2.2 volts per cell. A 12 volt battery has 6 cells. Also the amount of current drawn is during the few seconds that the bike is started. This is evident by the size of the cable going to starter, it is the largest on the bike. Every time you try to start or under load the voltage will drop.
Basically the path for the voltage to get to the starter is like this. There is a main fuse and may be other sub fuses. From there it goes through the ignition switch to run switch. From there it goes through the start switch which is a normally open switch you press to complete the circuit. From there it makes it's way to the starter relay. I think this is where your problem lies. This starter switch is normally in series with several other safety switches such as neutral position switch, kickstand switch (if available) and sometimes clutch switch. If any one of these switches are not properly engaged it will keep the starter from engaging. It is a safety feature.
Basically all this relay does is send power to the starter solenoid which is basically a magnetic switch capable of handling a lot of power for the starter. You can temporarily bypass this relay. Basically a relay has two potions. A coil side and contact. The coil side gets the voltage from the starter button when pressed. This magnetizes the relay and is the click you here, they are also spring loaded so it returns to starting position after you release the button. The side you are interested in is the contact side that sends current to solenoid. By placing a jumper across the terminals the starter should engage. Please be sure bike is in neutral and remove jumper if bike starts. If this method works you know the starter and solenoid are good. If not it probably is probably one of the safety circuits or the relay itself. Any or all of these circuits can be by passed but would advise against it. The safety circuits are usually two wires that can be easily tested with Digital Multimeter.
A friend of mine recently rode his bike after I diagnosed a bad voltage regulator/rectifier. He melted his ignition coils, blew his headlight, tail lights instrument lights, blew a hole in his CDI igniter and melted a few wires. I was able to diagnose all his problems with a Digital Multimeter and electrical schematics. If I can do it. Any one can. I know you can figure out the problem.
I hope this wasn't to much info. Just trying to be helpful. Don't let this get you down
Best of luck!