Windows 7 - Computer Died... trying to recover data from drive, windows won't show

My Sony Vaio (windows 7) died last night, after I dropped it in my garage getting out of the car. I removed the hard drive and installed it in an external case. I have it connected to my work laptop (dell windows 7) and I do hear the tone when I plug in the USB that tells me the computer noticed a new device. However, I do not see the drive available in explorer so I can copy my files.

After reading other posts I tried a few things with no success.

When I go into device manager I see "generic external USB device", and I have tried uninstall / scan for hardware changes. After a few minutes it changes back to "generic external USB device" so no good.

I go into disk management and I don't see the external drive at all.

What should I do next? Not an IT guy, just hoping I can recover my files. Any help you can provide would be greatly appreciated. Thank you in advance.

Update: I went back into disk management and I do see "Disk 1" now, but when I attempt to initialize I get the dialog box and it asks me for the partition style. No mater which option (MBR or GPT) I choose I get "Virtual Disk Manager - Incorrect Function" as an error message.

Check the hard drive with the manufacturer's diagnostic tools.
Hard Drive Diagnostics Tools and Utilities (Storage) - TACKtech Corp.
HD Diagnostic