@philsson - I used flasher3.5 to switch the phone into development mode, and I could then connect it to my (Linux) PC and copy the contents of the eMMC off it.

@htchang - The final update to my story was that it took 2 returns to Nokia to get a working N900. They never told me what was wrong with the original unit. Have you tried reflashing your phone? It sounds like yours isn't as badly broken as mine was. You might still have to resort to a warranty repair though.