Is there any way to retrieve pictures and contacts from a phone that was dropped in water and no longer turns on?

You can try to contact them and see what they can do.

Unfortunately, there is no way for us to save any of the data.

If the phone doesn't turn on at all, like it's not registering that it turns on, then there would be no way for us to get it turned on.

It needs power for us to be able to do anything, to get information off of it.

No, because if the power doesn't go to it, then there is nothing for us to repair, it would just be changing parts, and then you'll have no data on the phone.