Yes, bloodbanker. I suspect you need a step for the new site you added, and it should be fairly quick and painless.
Are you using iis? I will assume so, since you say you're on Windows. (The same concepts apply to apache, for those using that instead, whether on Windows or Linux.)
Look at your working intranet site in the iis ui, expand it to list its folders. You will see one there called jakarta. That's actually a "virtual" directory (vd) that got put there by the cf web server configuration tool (wsconfig) , which you or someone else there used to set things up before. Now look at the not-working extranet site. Is it missing that jakarta vd?
If so, it may be as simple as creating a new one by hand. Let me explain.
The virtual directory will point to to an isapi_redirect.dll file. You can see its full path by right-clicking on the jakarta vd, then choose "manage virtual directory" then "advanced settings". Copy the path shown at the top.
You may get by by simply creating a new jakarta vd in the extranet site. Right-click the site and choose "add virtual directory", with the name jakarta and the path/filename you copied.
Try your site. Does it work now? If so, great. It means that someone used cf's web server config (wsconfig) tool to connect "all sites" in iis to cf, and that set things up so that the needed settings to talk to cf (things in iis called isapi filters and handler mappings) got setup at the "server" level in iis. New sites inherit those. But there is no iis mechanism for a new iis site to inherit virtual directories that way, thus the need to create it manually.
If this approach does NOT work, it may instead be that whoever ran the wsconfig tool setup the intranet site separately, and did NOT set things up for "all sites". In that case, it would be best to remove that vd you added, then run the wsconfig tool instead and point it at your extranet site. But that's not something I'll detail here. It's in the cf docs.
And there's still more I could say, but let's see if this gets you going. I know many wish for one-paragraph answers. For some problems that's just not possible. 🙂