There are a variety of reasons this could be. One possibility is that, when you are doing a "full shutdown" you are really sending it to sleep. Most laptops now have their power button set to sleep by default. Try going to the start menu and select shut down.

If your already do so, then their are some computers that can startup from being shut down, but it is very odd that it would do so if you didn't configure it. It is an advanced feature usually. You can read the source for more info.

Lastly, it is possible your power button is stuck somehow. It may be turning on when something bumps it a little because it is stuck down. Clean around it a bit and make sure it is moving up and down like it should.

Best of luck!

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