If the motor was in neutral, the prop should not turn. Sometimes, they might turn a little is the shift is out of adjustment.
If it does not turn when in gear, then there could be a shift linkage adjustment issue, something wrong with the lower unit, or the prop.
As for the lights....you said no lights came on in the tiller handle.
Since your serial number starts with BAZL, that puts in somewhere between 1995 and 1999. The tiller handles in that timeframe did not have warning lights in the handle....they were in the lower cover. Therefore, someone may have retrofitted a more current arm to a remote model. So, there could be a wiring issue or possibly as compatibility problem.
If the lights are working and you have good oil pressure, the green light should come on while the motor is running to indicate good oil pressure. The only other light that you would have is the red overheat. The red will only come on if you have an overheat.
Sounds like the motor is new to you. If you are running the motor on a hose, besides using the standard earmuffs on the two water intakes, be sure to tape up the third water intake located above the propeller with duct tape. Otherwise, you could overheat the engine or mess up the impeller.
Mike