Diagnosis
This is a classic overheating or power failure symptom. The projector goes through its startup check, detects a problem (usually related to temperature or insufficient power), and shuts down to protect itself.
How to Fix It
First, rule out power. 1) Unplug the power adapter from the wall and from the projector. 2) Plug the adapter directly into a wall outlet—not a power strip or surge protector. 3) Check the DC power cord where it plugs into the projector. Make sure it's pushed in firmly and straight. A loose connection here can cause this exact issue. 4) Plug it all back in and try again.
If That Didn't Work
Let the projector sit unplugged in a cool room for a few hours to ensure it's completely cooled down. Then try starting it in the coolest room in your house, with all vents completely clear.
Heads Up
If it only works when cold and then dies after warming up for a minute, the internal thermal protection is likely kicking in due to a failed fan or clogged heatsink. This isn't something you can fix at home.