You are in a very tough spot, and you probably will not be able to recover it. I have not tested this, so it is only theory due to the last step, but here is how you would try:
First, if the computer you are using now, is the same one, everything you do risks overwriting the data. So try to move the disk to another computer for access there.
You first need to download and install a data recovery software, like DiskDigger.
After you scan for all the deleted and recoverable files on the disk, you need then need to find the registry hive the key was stored in, which was originally located in C:\Windows\System32\config (this is just for reference, as your file will probably not have a directory associated with it). You would be looking for the one called SYSTEM with no extension. There will likely be multiple copies to try with. Copy that file, or multiple copies, off the disk to the computer you are using to access the disk.
Then you would need to use a program that can read the encrypted location. This is the part I am not sure about because I have never used this software. Most of the key finders (Magic Jellybean Finder, etc.) assume that you want the local system, so you need one that you can specify and pick the registry file. This one claims to do that: http://www.magicaljellybean.com/keyfinder/ (note their note 3: "Load Hive option".
Overall, I don't think you have much chance, but this is the outline of how. Good luck.