You can indicate the new process should be started with elevated permissions by setting the Verb property of your startInfo object to 'runas', as follows:
startInfo.Verb="runas";This will cause Windows to behave as if the process has been started from Explorer with the "Run as Administrator" menu command.
This does mean the UAC prompt will come up and will need to be acknowledged by the user: if this is undesirable (for example because it would happen in the middle of a lengthy process), you'll need to run your entire host process with elevated permissions by embedding the appropriate manifest in your application to require the 'highestAvailable' execution level: this will cause the UAC prompt to appear as soon as your app is started, and cause all child processes to run with elevated permissions without additional prompting.