Press the power button and the home button at the same time. Hold till you see the Apple logo and let go
If that solution doesn't work......go to Apple.com and try calling customer support.
If you just "got it" and its within 14 days bring it back to the store and get a brand new one. or even another brand of phone if you decide an Apple is not for you.
The other suggestions are wonderful, try them as well.
I am sorry to hear of your iPhone 4 not powering on! To confirm some information, is this a new device? Are you within the 14 day worry free guarantee? If so, you should take it to the place of purchase to see about getting it replaced. If you need further assistance, please give a few more details.
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