If you're running SQL Server under the Local System account, it will not have rights to backup the database on a network share. You'll need to change the SQL Server account to perform such a backup.
Here's the procedure:
- Stop the SQL service.
- Go to Start>Run>services.msc
select MSSQLSERVER. Right click to choose 'Properties.'
- In the tabbed pane, choose 'LogOn.'
- Select 'This account.' Provide an account that has rights to access the shared network.
- Click 'OK.'
Restart SQL Server, and you will now be able to perform backups to any network share to which the account has sufficient permissions.