In the past, when I had this problem .. the workaround was to ..
Do a safe disconnect...
Leave the XHD running ..
Remove the USB cable ..
Wait a few ...
Then plug the USB back in (Hot) with the XHD running.
I was suspecting Plug n Pray problem .. but never found a fix.
I had several USB XHDs (same kind) .. but one always seemed to be undecided if it was USB 1 or 2.
Since the problem only happens with one computer .. I suspect you're thinking it's the computer.
From my past experiences .. I'm thinking it's the External.
By any chance .. Did you load any backup software that came with the "My Book" ???
I did this once and it messed up my computer .. I'll never do that again.
Not familiar with "My Book" .. don't these also come with Firewire ??
Sounds like it's time to go to WD's support here ..