The NMEA in to the radio is opto isolated inside the radio, so unless it has a problem the garmin should only see it as an led on the end of the wire.
The garmin on the other hand uses the 0v line as the return for the data.
So check that the data out and the radio have a one to one connection and there are no stray wires.
The garmin is obvioulsy getting loaded badly and is causing it to make a reset to end up with the garmin/garmin data selection.
Also, with the plotter disconnected and radio disconnected from the power, you should have no connection to either the red or black power input to the radio to either of the nmea input wires. Check with meter set to ohms.