Diagnosis
The motor is getting power and trying to run, but the mechanical lift mechanism is jammed. This is almost always because the desk frame is overloaded or the weight distribution is way off.
How to Fix It
Clear everything off the desk surface—monitors, laptop, that stack of books, everything. Then try the up and down buttons again. If it moves, you were over the weight limit. The Branch desk has a max capacity (check your model, but it's usually around 275 lbs for the dual-motor). That's the weight of the surface AND everything on it. Re-add items evenly, keeping the heaviest stuff centered over the legs.
If That Didn't Work
If it's still stuck empty, the internal overload protection might have tripped. Unplug the desk from power for a full 60 seconds. Plug it back in and try again. This resets the motor controller.
Heads Up
Don't just keep holding the button when it's humming. You can burn out the motor. If the reset doesn't work and it's empty, something inside the leg actuator is physically bound, and you'll need to contact Branch support.