fzabkar :
I would clone the drive, sector by sector, and then use data recovery software on the clone. Ddrescue is a free multi-pass cloning tool that understands how to work around bad media. It keeps a log, so it can resume after an interruption.
This is the most rational reply so far, except that the drive is spinning, not clicking, and is causing everything to freeze. Everything suggested above is only going to cause further degradation to your drive, which is why fzabkar suggested to clone the drive.
Recovery software scans the drive first then after it finds something then copies the data to another location. Immediately cloning the drive is going to get the available data off without wasting the life of the drive scanning. The problem moving to this before verifying the condition of the mechanical parts of the drive can also cause irreparable damage. This would be the first step that professional recovery companies like SERT Data Recovery or DriveSavers would take.
The key factor here is the failure was due to physical trauma or force. This will almost 100% of the time cause mechanical or physical failure. This will in turn most of the time require the drive to be opened and inspected for damage to the platters before continuing to spin the drive.
"To this point, the drive hangs every time I attempt to do anything with it." If the hard drive is spinning and not clicking but you get this type of error, then there is a good chance of head failure. If this is the case, it will require clean room repair on the drive before being able to clone the drive.
Here are some resources:
How to Know What Kind of Data Recovery
Using Data Recovery Software