Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
Pull the lamp out, hold down the blue button on your lamp door and keep it held down. Or you can jumper the holes on the white plug connected to the blue switch...that way you can turn it on.
Now...power it up. You'll hear the fans come on first, the color wheel will spin up making a wheeeee sound, then finally you'll hear the ballast fire 3 times before the TV shuts off and blinks its 3 lights. The ballast makes a Bzzzzzzzt sound, pauses for 15 - 20 seconds, then Bzzzzzts again.
These sounds are subtle, so do it in a quiet room.
Tell me if --
1] You do hear the fans
2] You do or don't hear the wheeeeee sound
3] You do or don't hear the Bzzzzzzzt occur 3 times before the TV shuts itself off.
Make sure you do this test when you know the TV will misbehave.
You can leave the door off the TV with the plug on the blue switch jumpered.
Examples of how you can jumper it --
Picture of the blue switch I mentioned --