"Display ads" are not simply an "old internet business model" they are the foundation of all advertising. So really Facebook lacks a business model the same way the trillion dollar tv and print industries lack business models.

The whole point of Facebook is to get users to spend all their time online there. At that point Facebook's business model can approximate any and all other web companies business models. Facebook's Search will be keyword based and charge Google-like rates per pageview. Facebook's app and content delivery platforms will take Apple/Netflix/Spotify sized cuts.