If a computer is on a home network hooked into a DSL or Cabel modem is the IP address of the external address of that modem stored anywhere on the PC. I only seem to get an internal 192.168.#.## from the registry.
Is there a router involved? Perhaps there would be an HTML document on the drive that was created when the router was configured which may show the external IP address….
If any changes were made to the router's configuration, there should be a saved file on the host that the router was accessed from. Unless it was saved to some external or removable storage. Most likely a .bin but it depends on the router.
If there is a router on the network, it was probably configured at one point – though this is usually over HTTP, and the resulting pages are usually marked "do not cache". If no physical router, then it's probably a newer cable/DSL modem that incorporates a router; these are usually not configured by the user.
I would perhaps look at applications that have a need to have external parties contact them – IRC clients, IM clients, and P2P software, for example. (Ideally you'd get the answer straight from the router or ISP, but that may not be an option.)