Diagnosis
The projector is failing its internal power-on self-test. A blinking red light is its way of telling you something's not right before it even tries to fire up the laser.
How to Fix It
First, unplug the power cord from the wall and from the back of the projector. Leave it completely disconnected for a full two minutes. This gives all the internal capacitors time to drain. While you're waiting, check the power cord for any kinks or damage. After two minutes, plug the cord firmly back into the projector first, then into the wall outlet. Make sure you're using the original power cord that came in the box. Now, press the power button on the projector itself, not the remote. Listen closely; you should hear the cooling fan start to spin up.
If That Didn't Work
If it still blinks red, the issue might be with the power supply sensing a problem. Try a different wall outlet on a different circuit in your house, like one in the kitchen or bathroom. Don't use a power strip or surge protector for this test—plug directly into the wall. If it works on another circuit, the original outlet might be faulty or underpowered.
Heads Up
If it only works on the remote and not the physical button, that's a different problem—likely a stuck or faulty power button on the unit itself, which would need service.