Glarysoft is giving away a program called "Amazing Dr. Recovery 3.1" on their web site at:
Giveaway - Glarysoft

The download is a .ZIP file of about 4.5 Megabytes.
You unzip it to create a folder that contains a Glarysoft installation program and a ReadMe file. The Glarysoft installation program connects to the internet and installs the file recovery program on your computer. The ReadMe file will have the activation key. To activate the program, CTRL-C copy the activation code and click on the "Activate" link in the opened file recovery program. The program will ask for the activation key. CTRL-V paste the activation code in. The program will respond to tell you if the activation was successful.

I used this Amazing Dr. Recovery 3.1 on my USB drive with the corrupted FAT table, and it successfully found and recovered all of the files on that USB drive.