This means you must authenticate on the PC first using the web interface then get access. For this kind of access there is no distro or dd-wrt firmware that I know of that will handle this. Your options then would be free sharing apps like Proxy+ or old time app called Proksi. Anyways - can't help you there. If your thing could authenticate using MAC you could work something out using MAC cloning or so.
Knowing the solution doesn't mean knowing the method. Yet answering correctly and regurgitation are considered "learning" and "knowledge".