Diagnosis
The control panel/display unit has lost power, but the main board or motor might still be getting juice, hence the hum. This often points to a blown fuse on the control unit or a loose internal connection, not a total machine failure.
How to Fix It
First, do a hard reset. Turn off the circuit breaker that powers the dishwasher for a full 2 minutes. Turn it back on. This can sometimes reboot the electronics. If the display stays dark, the next step is to check the in-line fuse. You'll need to unplug the machine or switch off its breaker, then remove the kick plate at the bottom. Look for a small, clear plastic fuse holder in the wiring near the front. Check the fuse inside with a multimeter for continuity. If it's blown, replace it with an identical 5x20mm, 5A, 250V time-delay (slow-blow) fuse.
If That Didn't Work
The issue could be the control panel itself or its main ribbon cable connection. This requires removing the inner door panel to inspect. If you see any signs of moisture or corrosion on the connector, that's your culprit. A disconnected ribbon cable would cause this exact black-screen-with-hum symptom.
Heads Up
That faint hum you hear could be the water inlet valve stuck open, slowly letting water in. If you suspect this, turn off the water supply to the dishwasher immediately to prevent a flood while you diagnose the display issue.