A very good write up by Matthew Boyd on recovering data from a failing BitLocker Drive.
http://iboyd.net/index.php/2012/09/08/recovering-data-from-a-failing-bitlocker-hard-drive/
TL;DR version:
Removing the disk drive from the laptop/PC and connecting it via USB to another Win7/8 PC will allow you to attempt to access the data with the Recovery Key.
If this fails or has problems,
RIPLinux with DDRescue can make a copy of the data to another disk in the hope that you can gain access to the data from this new disk.