You can't spawn processes on the client machine from server-side code.
When you use Process.Start in server-side code, it is attempting to execute the process there, on the server where the website is hosted. If you wanted to create processes on the clients computer then you would need to expose a download for them (and not in employing subterfuge, like malign sites might do to install software - supply it gracefully, and normally (and with permission)), or a Silverlight application or something along those lines.
The bottom line is that the code you want to execute (even if that is just to spawn a process) must reside on the client, and be executed there.
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