By not dismounting the HDD on the Vista System. You need to use the Safely Remove Option on every External HDD before unplugging it or turning the system off.
Turning the system off doesn't send the External HDD the correct signal to shut down it just removes the power and leaves the HDD to it's own devices to park the Heads and make the drive safe. You may get away with running CHKDSK on the External Drive to repair the File Structure but it just as likely may not work and then you'll need to employ some form of Data Recovery Software that can rebuild the Partition Tables.
If the data is [b]Important[/b] as apposed to being [b]Nice[/b] to get back you really should send this drive to a specialist Data Recovery House and pay them to recover the Data off it. However if you can accept loosing the data you can try one of the software alternatives here is a very short list of some that are available.
http://tinyurl.com/273ay5
http://tinyurl.com/rmvrv
http://tinyurl.com/yvrsl
http://tinyurl.com/yyk8cm
http://tinyurl.com/382vm
http://tinyurl.com/ynwnel
http://tinyurl.com/nc4kx
http://tinyurl.com/2wox7l
http://tinyurl.com/374d8b
http://tinyurl.com/djw6u
http://tinyurl.com/f73se
http://tinyurl.com/8bd3f
http://tinyurl.com/afu2j
While the last 2 are from the same company they are very different products. Win Hex should only be considered for use by someone who knows Hex Inside Out while Davory is a great cheap General Purpose Application.
Personally I prefer the On Track Option but it's anything but cheap. However because I use this type of software a lot it's paid for itself many times over by now, for a cheaper option Spin Rite from Gibson Research or Stella have both very good reputations by other TR members.
Col