Diagnosis
The unit is in "fan only" mode, or a safety delay or fault is preventing the compressor from starting. There's a 3-5 minute delay between turning it on and the compressor engaging to protect the system.
How to Fix It
First, check your settings. Make sure you have it set to a humidity level below the current room humidity (try 50%) and that it's not on a "Fan Only" or "Dryer" setting if it has one. Then, just wait. Let it sit, fan running, for a full 10 minutes. If the room is already at or below your set humidity, the compressor won't turn on at all—that's normal.
If That Didn't Work
If after a long wait in a humid room it still doesn't click on and get cold, the compressor start capacitor is a likely suspect. It's a common failure point. You can sometimes hear a faint click or hum if the capacitor is trying but failing to start the compressor.
Heads Up
Troubleshooting capacitors involves dealing with high voltage, even when unplugged. That's a job for someone with electrical repair experience.