Community Wiki answer added to document contributions originally left as comments
From KASSQLDBA:
As per the posted error, it seems like the file may be corrupted. Please read the following to see if it helps:
Affordable Solution To Repair Corrupt SQL Backup File (TechNet Gallery Third-Party tool)
From Kin:
Can you copy the backup to another drive NOT
C:\and then try to restore it? If it fails, its definitely corrupted and you are out of luck.
See also SQL Server Troubleshooting: How to detect and speedily fix SQL Database corruption on Microsoft TechNet.