iPhone 5s won't turn on would want it fixed - possible board problem

Hi, may I know if I can send over my iPhone 5s to have it fixed? How much would it cost? Problem: iPhone 5s battery was drained after being used for 1 day. Placed in charger to charge. Phone stuck in Apple logo. Tried to update with iTunes get error 51. iPhone now won't turn on (black screen - leds visible on). Replaced battery, now phone won't turn on.