My e10 won't turn on, with fresh batteries, and it hasn't gotten wet.

Take a pencil eraser and clean your battery contacts. Next, I'd consider that perhaps you may have condensation in your camera and this can cause the kind of behavior you're talking about. You can place the camera in a ziplock bag with a cup of uncooked rice. The rice will act as a "dessicant," and draw out moisture from the camera. But if you dropped the camera while on the trip and after turning it on it got stuck, you may also be dealing with a lens out of alignment.

One thing you don't want to do is force the issue. Send it in for a repair estimate. But understand that the average cost of a camera repair is around $180. As such, it may cost more to repair than it is really worth. The rule of thumb is that if the estimate for repair is north of 50% what you paid for it, you're better off taking that money and buying a newer and upgraded model.