If the patch is an MSI package, you can use Active Directory to push the update to computers on the same network that are running an AD server. The update will be performed immediately or at the next start.
You can push packets yourself, but there must be some kind of transport mechanism that is listened on the other end, controlled by the program with sufficient skills and privileges for automatic updates.
Ban AD, this is probably your best shot: use regular network files to bring the update to the client. The client computer MUST work, but it may be on the welcome screen. Then place the batch file in the Documents and Users / All Users / Start / Startup folder, in which the MSI will complete the installation (basically, telling MSI to perform an unattended installation with the default installation options) . The next time you log in, the batch file will be launched, performing the installation. After that, MSI should possibly clear the batch file. If you can remotely access the registry of the client computer (I doubt it very much), you can put the batch file in the temp directory somewhere and put a link to it in the RunOnce registry folder.
After going through this rigamarole, you will probably teach you how to structure such applications to check and download your own updates through a well-known web service or configure them to use ClickOnce deployments (this does the installation boot directories, but deploying updates becomes MUCH simple).
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