If you are not using a Real-Time target, you should have not trouble publishing your front panel to the web and controlling it from a remote computer with only LabVIEW Run-Time installed. Here is what you need to do:
1. On the host computer with the finished VI, go to
Tools->Options, select
Web Server: Configuration, and enable the web server.
2. Then open up
Tools->WebPublishing Tool, select your VI and the other properties you wish it to have, and save to disk
3. You now should be able to go to your remote computer and browse to http://HOST IP ADDRESS/VI NAME.html and view the front panel. You can right-click on the front panel and Request Control of the VI.
Hope this helps!
Brian T