Does it have trouble turning on when it hasn't been on for a while, or only after it has shut itself down? Kinda sounds like a heat issue to me but I'm no expert. If it still has trouble turning on even when completely cool, that would probably eliminate that possibility.
The first time I noticed it it would not turn on though it had been off for over a day. However, the last time I turned it on it turned on with some ease. Shut off after maybe 1-2 minutes -- enough time to start google chrome and check reddit very briefly.
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