I believe what you are trying to achieve is not possible!
If I understand correctly, you wish to elevate the currently running process to perform some tasks by the new dialog that requires Administrator privileges.
You can see that various programs that utilize UAC actually launch a
separate process each time an administrative action needs to be performed like TaskManager.
If you wish to elevate a process you are starting, you can use the
StartInfo.Verb = "runas":
...
startInfo.Verb = "runas";
System.Diagnostics.Process.Start (startInfo);
You could however perform operations
on behalf of a different user, using
Impersonation
See
A small C# Class for impersonating a User[
^]
Good luck,
Edo