Moto X micro usb port not charging.

My Moto X suddenly stopped charging last night. I have attempted to charge it with several micro USB chargers with no success. Momentarily, if i plunged the charger into the phone and then held the charger at the very same time allowing the phone to angle down and the top of the usb to connect to the ceiling of the m-usb port, I got a few seconds of charge but never enough for the phone to start. As of now there isn't an angle or charger that will charge my completely dead phone. Can the usb port be replaced, can I do this or better yet, is there a service "out there" that can fix this for me. I can have the phone replaced by Motorola but do not want to lose a bunch of "private" photos or rather important text messages from work. It does have a micro USB card but I am not sure how much was being stored on that card. Thanks in advance for your assistance.