This may sound silly, but I've actually had success with it several times: Change the drive orientation prior to booting. If you normally keep it horizontal (and it's no longer booting in that position), turn it to vertical before powering up.
Note: This has never worked more than once on any drive it's been successful with. If it works, make darn sure you're ready to copy the data RIGHT NOW.
Certainly doesn't work all the time, but it costs nothing to try it...
-------------------- In the Land of Eternal Light Pollution & Great Pizza (Chicago)
SN-6, ED80, WO 66SD
Meade 208xt, SBIG ST-4
D70 (modified)
CGE (way modified)
A Wife who understands (unmodified)
Some other stuff...
I may not have gone where I intended to go, but I think I have ended up where I needed to be. Douglas Adams