OK it sounds like there is a remote start installed here, lock and unlock the drivers door again and try turning the engine off with the key.
Pull the black box and its wires out from under the column cutting the wire ties to get it out as far as possible without disconnecting any wires and see if there is a smaller square relay that the wiring from the box runs to. This is the relay that sends the start signal to the engine computer from the ignition switch and the remote starter.
There should be two wires from this relay that run to the black box and two more that each run to a yellow wire, cut at the yellow wire ends and join them with a crimp connector or solder and insulate the connection.
All the other wiring to the black box can be disconnected from the vehicle but see if there is a name, model number anything that will tell me whose alarm this is and what model. If I can get a brand and model I can get a wiring diagram to help you with the removal.
If you cannot get the engine to stop you can pull the auto shut down relay from the fuse panel and this will shut the engine off.
Click here for relay
This is a step by step process as I can't see how this was installed and every installation is different.
Do you still have the remote for this?
Does it have a name? Is it a remote start?