You should hear a boot sound or feel a vibration. The easiest way to check this is to long-press the power button to force it to shut off and then turn it back on. This is the next possibility, the phone is actually on but the display isn't working. Seriously, though - did you charge it lately? / © NextPit Remember, sometimes you need to charge for a few minutes before your phone can power itself on. Grab a power supply and make sure you actually have some juice on your phone before we proceed.
Just kidding - but seriously, when was the last time you charged it? Sometimes time flies when you're having fun watching cat videos and the next time you pick your phone up it won't turn on because you've YouTubed it to death.