If the ClickOnce application is set to Full Trust, during installation it will ask the user to provide full trust. This means that the application will have all the same privileges on the computer as the user running the application (editing the registry, io file, etc.). You mentioned in the comments that the application is configured for full trust, so this does not seem to be a security issue.
Are you sure all the necessary files are being deployed? I will simply remove ClickOnce from the image. Look at all the files in your deployment, create a folder and copy all these files into it, and then try to run it. It works? My initial guess is that some of the required files are not included in the ClickOnce deployment.