Various Antarctic territorial claims provide "land borders" that cannot be crossed due to the lack of roads, including:
- Australia & New Zealand (160°E)
- Australia & France (142°2′E and 136°11′E)
- Australia & Norway (44°38′E)
- Norway & United Kingdom (20°E)
None of these countries share a land border anywhere else in the world, of course. EDIT: As was pointed out by Nate Eldridge in the comments, it is possible to drive from Norway to Gibraltar, which is also a British Overseas Territory; so the last of these does not qualify.
For the purposes of this question, it is probably best to draw a discreet veil over the conflicts between the claims of Chile, Argentina, and the UK, as they make the concept of a "border" ill-defined. The Chile-Argentina border on the South American continent is relatively easy to cross anyhow.