Is the hard drive under warranty? If not open the the external case and connect it directly to the system. If still under warranty don't break anything.
1. Replace cable used to connect external HDD
2. Run EaseUS Partition Recovery(free) http://easeus.com/resource/partition-recovery.htm
If you can find the partition you will be able to restore it..If not you will have to use a data recovery software to get the data off. Runtime & r-studio make good apps.