OP – at a guess, your external website is not managed or hosted by your company directly, you get an agency to do it?
If so, I wouls specualte that, as you use Active Directory, that uses a private version of the same Domain Name System (DNS) as the Internet and somebody has put a static entry in there that points to your website on the Internet as, otherwise, your private DNS would tell all your work computers to look internally for the website.
In the meantime, the agency have moved the server that is running your inaccessible website and happily updated the Internets DNS system, so the public can get access but, because you have an old (now incorrect) entry on your private DNS, you can’t see it.
As stated above, I would put a bet on using the nslookup command to get an IP address for the site from your private work network and elsewhere return different addresses.
Rachel