Diagnosis
Either a faulty connection between the adapter and the projector, or the internal power board has an issue.
How to Fix It
First, check the proprietary magnetic connector. Unplug it from the back of the projector, inspect for any bent pins or debris, and reconnect it firmly until it clicks. Try the power button again.
If That Didn't Work
Perform a hard reset. Unplug the power adapter from the wall AND from the projector. Press and hold the physical power button on the projector for 30 seconds. Reconnect everything and try to power on.
Heads Up
Only use the official 65W Samsung adapter. A third-party charger might provide enough power to light the adapter LED but not to boot the projector, causing this exact symptom.