How can I recover images and videos from a broken Droid Turbo?

Episode 1211 (1:42:17)

Victor from Camarillo, CA
Droid Turbo

Victor bought a Droid Turbo and took a lot of pictures and videos of a graduation ceremony. But after a couple days, Victor wasn't able to get the phone to turn on. Only half of his photos and videos got up to the cloud. How can he get the rest off the phone?

Leo says that DriveSavers can do it, but it won't be cheap. It also depends on the failure. If the OS failed, then the data should still be there.