What I did once was to create a WebService (the functionality was encapsulated anyway) and indicated the method as "OneWay", which basically is "Fire and Forget."
http://msdn.microsoft.com/en-us/library/ms181848(v=vs.80).aspx
Your request goes without waiting for a response from the server.
Of course, you need to encode your own βnotificationβ logic so that the user knows about the success / failure of the task.
As pointed out in the comments to @stefano, you can use Diagnostics.
http://msdn.microsoft.com/en-us/library/system.diagnostics.process.start.aspx
Since this will be in OneWay setup, your web application will not wait for the application to complete before the release of HttpResponse.
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