The error messsage is reporting a file system problem which is part of the OS and not a hardware problem.
Run "chkdsk C: /F" and reboot. Chkdsk can't be run under Windows so when you reboot it will run before windows loads. Chkdsk may take a while but be sure to let it run all the way through. When it is complete reboot again, log in, and try to shrink the disk parition again.