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Most 27 inch Sony's don't have a button to push....If you turn off your TV for 20 minutes and turn it back on, you should hear a "Bong!" sound at startup.....that's your built-in degausser doing it's job, but it fires only when the TV is Cold.....If you don't hear a "Bong" then most likely your degausser needs resoldered due to bad connections.
It's unlikely, but your symptoms also describe a loose yoke, or a bad shadow mask. A good technician will have a test for both problems.
24 years servicing various brands of TV's including Sony.