iphone 4s won't turn on

my phone 4 months old , didn't jailbreak it. using hour ago , had 20% battery. picked make call , won't turn on/go lock screen/etc. didn't drop it, wet. . .didn't it, put in purse, came in hour, , nothing! out there can helfp!!!
*i don't have applecare+, so, if it's totally dead apple/at&t me?? since it's 4 months old!!!

 

have tried plugging in awhile?

 

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