There are levels of "does not respond":
- Can't boot from it, but the computer otherwise does not report errors.
- The computer reports "no disk".
- The disk makes loud clacking noises.
- In addition to #3, there is visible smoke and/or sparks.
If the situation is #1 or #2, have you tried reading the disk with another computer? Putting in in a powered USB (or equivalent) enclosure and seeing if another computer can read it might work.
#3 is bad news, the drive might not be recoverable at all. #4 is very bad™
Assuming you can't read it on another computer, and there is no visible smoke, the only thing you can do is send it to a professional outfit that does forensic level recovery. Ontrack (now "Kroll Ontrack") has historically been the big gun in that industry. I have used them in the past, they are expensive but if the data is on the drive they can recover it. I have also heard of SalvageData and TTR Data Recovery, but I have never used them.
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