trying to run a process from an asp.net application

Answer 1

Try creating a new app pool with a a new admin account. If that works remove the user from the admin group and create a new group with the necessary permissions for the app.

Answer 2

I've tried to run on my local IIS with copying test console app into bin directory of web site and it works:

        string path = "bin/test.exe";
        try
        {
            ProcessStartInfo pi = new ProcessStartInfo();
            pi.UseShellExecute = true;
            pi.FileName = Server.MapPath(path);
            System.Diagnostics.Process.Start(pi);
            lbl.Text = "Started Process: " + Server.MapPath(path);
        }
        catch (Exception ex)
        {
            lbl.Text = ex.Message + 
            "<br/><p>" + ex.StackTrace + "</p>" +
            Server.MapPath(path);
        }