a hit counter to know if the site's been visited - they aren't a reliable indicator anyway. Hit counters work by recording each occasion on which the page concerned is loaded into your browser. Go to a site with a hit counter and click back and forth between different pages. You'll see the counter notching up each time the page is loaded, and you can raise the count with no problem.
Better to rely on the web host's server statistics. These will be detailed and accurate, and will even tell you which browser the vistors were using. You can usually get the host to turn server stats on for your site - just ask them. They'll give you a url for the statistics, and you can see them in Internet Explorer whenever you wish.