'01 S4 and all '02 and later Monsters had the IAW5.9 ECU, which directly controls the signal to the starter solenoid.
The ECU checks a group of sensors to determine if it's safe to start the motor.
All Monsters prior to that had direct button-to-solenoid wiring.
I've seen that behavior from damaged ECU's.
Yup. What's interesting however is that the bike still will not start if those sensors are tripped. The starter will now crank, but the bike still won't start. For instance, if the kill switch is in the OFF position, my starter will crank, but the bike will never start (no spark?). Or if the kickstand is down with the bike in gear... same business. Bike will start in gear.. but obviously stalls out after a small jerk...
Not the safest, i know, but an ECU isn't in the budget for this year.