Or Reliable in most peoples books.
But in answer to your question the HDD has had it's MBR's corrupted that is why you are unable to access it on any computer this happens when you regularly unplug without using the Safe Remove Option.
As you say this is Valuable Data it is possible to recover it but how much are you willing to Pay for the Privilege and more importantly How Much time are you willing to spend to achieve the Recovery?
Depending on your Answer to the above you can use something like On Tracks Recovery Software that will rebuild the MBR's in a few minutes but the down side is that it's going to cost you about $1,200.00 for the application. At the other end of the Data Recovery Software there is something like X Ways Davory which is about 35 Euros but only recovers by file type so you need to format and then run the recovery program over the Currently Blank HDD and save the output to another Drive. Takes anything up to 3 days to recover one file type and then you need to start on the next. The Recovered Files are not saved by their old name but by Numbers as the software starts with file 1 and works through to the last file of that type on the HDD some are incomplete and others are what you want but you need to find them first.
Here is a list of the more popular Data Recovery Software that is available but it is by no means a full list of all that is 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 foe 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