There's no way to automatically differentiate between computers based on IP or even MAC addresses.
One thing that could work for authenticating that the user is who they say they are is to use an "image" key. Give them an "avatar" that isn't their avatar (i.e. has to be picked from your set, can't be uploaded) and then enter a secret phrase. Then when they log in again, you ask them to choose which picture and fill in the passphrase. If either don't match, you know it's not the same person. Some banks do this (well, half of it).
Other than that, there's no way to differentiate between me or my girlfriend using this forum (not that she would 😛 ) because we're using the same internet line. The only chance of differentiating computers would be MAC addresses; but, even they can be cloned.