The desktop is not C:\.
The desktop is a folder C:\Users\<logged in user>\Desktop. So that's where you need to write the backup, and you need to ensure that the SQL Server service has full control of that folder (and that there are no other security restrictions from windows)
Why does it have to be the desktop?
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability