Easy fix...I don't know about that unless you can perhaps jar it loose with a needle, but I do know that accidental damage is NOT covered by limited warranty. You might try an Apple store, provided one is near you.
I suspect it can be fixed, but if the needle idea doesn't work, not easy. Another alternative is to take it to a iPhone repair shop, they should be able to get it working. Apple will probably tell you it is not repairable and get you to buy a refurbished out of warranty replacement. That is great, but more expensive than paying a shop to open up the iPhone and fix the problem - assuming nothing else broke inside.
I will second that a drop will not be covered by the limited warranty. It would have been covered by Apple Care + if you bought that with the phone.
It is definitely not an easy fix. I've worked on them some and it's not for the weak of heart. I do have a workaround for you to get you going for now. If you go to 'Settings' then to 'General' then to 'Accessibility', then scroll all the way down to 'Assistive Touch', and turn that on, it will give you an on screen button that will let you control different things. Once you have that you can go to 'Device' and hold down 'Lock Screen' and the phone will power down. Now since the power button doesn't work, whenever you want to turn it back on, plug it into a charger and it will power up automatically.
Long answer, but it'll get you out of a bind if you need it.