How to access files and folders in a damaged hard disk?

Solution 1:

There's a difference between physical corruption (bad blocks, surface errors, wear out due to age, etc) and logical errors, where the hardware is perfectly fine but the data structure to the files is damaged and the system can't read the files. Files deleted by accident can be considered to be in the second category.

Any data recovery software will be of use only in the second case. Nothing can help you if your HDD is physically damaged (well, there are some extreme measures, such as replacing the logical board, but it's stuff not to be done at home).

In your case, your seem to be having both physical and logical issues. I recommend you use Recuva (or another data recovery tool) to copy the files to a second, separate HD - remember, never perform data recovery saving the files to the same HDD.

As for your specific case, in order to use Recuva to recover files that weren't deleted but just unacessible, mark the "scan for non-deleted files" checkbox, see image below:

Solution 2:

You may want to try a Linux distro in Live mode. Specifically, a "Rescue Disk." Based on the brief descriptions there, Plop Linux might be your best bet, but don't hesitate to try more than one.

Solution 3:

If you're willing to spend some money, you can pay a data recovery company to look at the hard drive for you.