OK, so a static IP is not an option 🙂
Active X is, but I'm afraid I know nothing about it.
Writing an exe is as well, but you would have to design it carefully. The exe will still have to send details to a form on your website, so once anyone discovers what details are being sent to the website, they can just send those details without usin the exe.
Cookies, as I have described, might be an option.
Another option would be to configure your browser in a special way. One example would be (if your browser is Firefox) to go into Tolls->Options-General->Languages and add an unusual combination of languages eg Welsh and Xhosa to the bottom of the list. Do this on each of your "approved" PC's. This shouldn't affect browing of normal sites, but your site could scroll through the requested languages and only allow people in if they have these lanuages set. Your script can see which languages the user has requested in the variable $_SERVER["HTTP_ACCEPT_LANGUAGE"] where they are stored as a semi-colon separated list.