Which OS are you talking about?
XP? Vista? Seven? Windows 9x/me?
So your want it so that there is no web-browsing possible at all on this
computer. In that case, it is probably possible to remove all links to
Internet Exploiter from the desktop and all start menus, and even to
rename the IE executable file so that it cannot be invoked by the user.
Only when the system is using the DNS service, which by and large there
really is no reason for that service to be running on the typical
NT-based OS these days.
Because they assume you are running the DNS service - which you do not
have to, and for which I disable on any XP systems I administer or
setup.
Again, if the goal is that there is no web browsing to be done on the
machine, then you can achieve that by
1) not installing any web browser on the system (firefox, opera, etc)
2) removing all links to Internet Exploiter. This includes desktop
links, start-menu links, etc.
3) rename the IE program executable so that it cannot be run via the
start-run method.