DIAGNOSIS The unit is in "fan only" mode, or something is preventing the compressor from engaging. First, check that you don't have it set to a specific humidity level that's already been met. If the room is already at or below your set point, the compressor won't cycle on.
FIX Set the unit to "Continuous" mode and set the fan to "High." This should command the compressor to run regardless of humidity. Listen for a click about 3 minutes after turning it on—that's the compressor relay. If you hear the click but no compressor hum, the relay might be bad or the compressor might be seized. If you hear no click, the control board isn't sending the signal.
IF THAT DIDN'T WORK A very common fail point is the start capacitor for the compressor. It's a small cylindrical component that gives the compressor the extra jolt to start spinning. If it's bulging or dead, the compressor will just hum or do nothing. Replacing this capacitor is a standard repair, but you must discharge it safely and match the microfarad (µF) and voltage ratings exactly.
HEADS UP Working with capacitors and live mains voltage is dangerous. If you're not confident, take it to a repair shop. A bad capacitor is a $15 part and 10 minutes of labor for a pro.