Earth was the computer before the Vogons destroyed it. Earth2.0 was what Slartibartfast was building for the mice. Just providing computer names from within the book. Deepthought can still exist even if the user replaces it with a new computer.
I wish TV stations would rerun the BBC serialization of Hitchhiker's. I've actually read Adams' books but it'd be nice to see the TV version again. (I used to love Peter Jones as The Book, his matter-of-fact tone made him just ideal for the job.)
Never did think of an appropriate name for the new desktop though.
edit: thanks for all of the suggestions!