Diagnosis
The most common cause for a continuously running vent fan on a Samsung ME19R7041FS microwave is a malfunction in the touch control panel. Grease, moisture, or food debris can create a false electrical contact, making the unit think the vent "On" button is being held down. A less common, but more serious, cause is a failure on the main control board, such as a stuck relay that powers the fan circuit.
How to Fix It
First, unplug the microwave for safety. Thoroughly clean the entire glass touch control panel with a soft cloth dampened with a mild, non-abrasive cleaner or a 50/50 mix of water and isopropyl alcohol. Pay special attention to the vent control buttons. Wipe dry with a clean cloth and allow it to air dry completely for 10-15 minutes. Plug the unit back in and firmly press the vent "Off" button several times to clear any residual signal.
If That Didn't Work
If cleaning doesn't resolve the issue, the problem is internal. You will need to unplug the microwave and call for service. The technician will likely need to replace the main control board (PCB), which has likely developed a fault that is sending constant power to the vent fan motor. Do not attempt to remove the outer casing yourself due to the high-voltage capacitor inside.
Heads Up
Leaving the fan running constantly wastes energy, creates unnecessary noise, and will prematurely wear out the fan motor. Unplugging the unit is the only way to stop the fan until a permanent repair is made.