Assuming you have already swapped the USB cable.
If you desperately need the data, there is one approach to this that you haven't tried yet. It involves carefully removing the hard drive from the external enclosure and attaching it to a(desktop computer/tower) which has an available SATA port on the motherboard. You attach the drive as an extra drive on the highest SATA port, so if you have say 4 SATA ports on the motherboard, 0,1,2,3 ... you connect it to SATA port 3 for best results so that this drive is not seen by the system as a bootable drive.
To do this you have to carefully remove the hard drive from the external enclosure, which in some cases means that you end up destroying the enclosure in the process. Some enclosures have screws that make removing the hard drive easy, while others either are snap together clam shells which sometimes have ejection slots for a flat headed screw driver to apply pressure and release the snap lock plastic tabs, and others are combination of both screws and locking plastic snap tabs, and in some uncommon situations the drives were never meant to ever come out of the enclosure and its a non-serviceable snap tight enclosure. These you end up having to carefully find the seam, and wedge a screw driver into them and pry at the platic to break away the plastic and create a hole in the plastic without damaging the drive inside. (so you dont want your tools reaching into the enclosure far enough to damage the drive, and you also do not want to take a hammer or use any other type of hitting force to break it open as for this will likely destroy the drive inside.) One a hole is started in the plastic, you can take a pair of pliers or dikes and break away more and more plastic bending it and tearing it open.
Once the drive is exposed, removal is usually very simple a couple screws and its out when carefully unplugged from the SATA Power/Communications board that is inside.
- This process will eliminate having to worry about USB/SATA communications conversion which some tools can not handle, when they were designed for local drive access.
- If its as simple as the USB/SATA com board dying in the enclosure from as a static discharge etc, then you may have instant access to your data without having to use any data recovery tools. This would be the best thing to happen for you at this point!
- If you are still unable to access your data now with drive attached locally without USB conversion, and trying all tools suggested again, then the only other options are to pay for the expensive process by a data recovery center to recover the data or take a total data loss and start over with a new external drive, without trust in this drive if you are able to format it and use it ever again.
* For all important data its best to have at least 2 backups of the data. This way when something like this happens its highly unlikely that both drives would die at the same time. Many people put all their eggs in one basket and get bit by total data losses. It has happened to myself before with a single point of data failure as well as I am sure others here. For extremely important data, I also burn the data to DVD and place it into a jewel case in a shoebox with a small notebook with a number on the DVD and Date of the Burn, so I can quickly index where important data is in my DVD Data Archive if I need to access it. And this came in very handy when I needed to look up my ebay business information the one day from an investment I made in which in order to not get over taxed on a short term gain, I had to find the PDF of the purchase price on the invoice for the item that I bought that I ended up selling for much more. If I didnt have this documentation, uncle sam would assume that it was 100% profit and I would have taken a significant profit margin loss.