I dropped my iPhone 5c and it wont turn on but its constantly vibrating. I have tried holding the home and lock screen for a long time but nothing has happened. How can I fix this?

You make an appointment at the genius bar of your local Apple Store and get it serviced/replaced. You broke it. If you can't even force a reboot, there's nothing much more you can do.

It going to cost you $269 + tax unless you have apple care plus but that is correct you will need to either contact apple care at 1-800-692-7753 or visit an apple retail store.