The System.Diagnostics assembly is part of the Silverlight CLR framework, but it only includes classes related to debugging, the Process class is not available. Is there any
If you are running your application either in the browser or as a standard out of browser application, being able to start another process would break the Silverlight model, allowing your application access to the machine outside the browser sandbox.
A full trust application will be able to do this.
Why do you want to start another process?