I updated my ClickOnce application and then when the user runs they are asked if they want to install the new version.
I am working in a highly controlled environment. When an update is available it has to be installed (backwards compatibility with the database is not ensured with old versions).
Another option is to fail the run if skip is pressed (that works fine too).
I need some way to stop them from running an old version of the application.
This article answers your question. I'm pointing you to the article instead of just posting an answer because everything in the article is worth knowing.
http://www.sayedhashimi.com/CategoryView,category,ClickOnce.aspx
The following is the relevant excerpt from the article:
I also found another good article:
ClickOnce: Bringing Ease and Reliability to Smart Client Deployment