Does it display the Apple logo for a sec and then reboot again?
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=== Update (09/08/2017) ===
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If it never gets to the Apple logo then it's probably dead from a power standpoint. If it won't power on at all, or only via external power it will boot to the Apple logo and then power itself back off (and eventually back on again), then it's detecting a fault of some sort on the boot up (i.e. when you see the Apple logo it's doing a sort of pre-flight systems checklist).
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I saw this sort of thing on three iPhones over the summer (4S, 5, and 5S) - and of the two I've fixed so far, one (the 5) required a new battery, and the other (4S) I was able to get going again by charging it with an Apple cable and charger.
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The issue in my case with the 4S was that it had run down so far that the phone thought the battery had gone bad. There are more severe hardware issues that can cause this sort of thing, and as well there are potential software issues that a hard reset might resolve, but for me 2 out of 3 of these (so far) were either bad or over-drained batteries.