I think you're missing a bunch of things about the fundamental architecture of ASP. ASP executes on the server as an ISAPI extension to IIS. Clients never even know it happened. In fact, IIS prevents clients from ever getting the raw code themselves. If they did get the code, they wouldn't be able to do anything with it without loading it up on to their own IIS server (since classic ASP is an IIS ISAPI extension, as we already mentioned).
So, your problem is somewhere on the server. The error message you're receiving says you have a problem with a registered type library. I doubt ADODB is not registered, so I would be inclined to check anywhere else I'm newing up an instance of an external type. I would also be looking at RegMon/ProcMon/FileMon for access denial issues, specifically with COM/COM+ attempts.