I'd try a Linux Live CD/USB (probably ubuntu) - then use something simple like "dd" to take a full image of the device.
A command like this may do the job
sudo dd if=/dev/sdx of=/location/you/want/the/image.img
/dev/sdx needs to be the label of your dodgy USB stick. It will be something like sda, sdb, sdc etc (probably the later letter)
If all that works I'd then transfer the .img to a Windows system and mount it with a drive image mounter (Virtual Clone Drive) and see if that works.
EDITED: 18 Mar 2015 21:41 by ANT_THOMAS