That is a cable with double USB power, not a powered hub. Not the same thing. Still better than nothing if you have no powered USB hub at hand, though.
Is it still under warranty? This is the appropriate time to RMA it back and get it repaired/swapped at their expense.
If it is not under warranty, and none posts better ideas (I really hope someone else does, but if the computer cannot even connect to the drive... there isn't a lot to do), you can try opening the case and taking out the HDD, and then connecting it to a desktop computer as if it was an internal HDD (because it is
an internal hdd without the case)
and then see if it works there.
If it works fine (and hopefully your files should still be there), then you buy an External enclosure
of your liking (even a fancy USB 3.0 or eSata one if you have the right ports on your laptop) and place the HDD into it.
It is a bit time-intensive and you may not be able to open the original case without damaging it, so it's really the last thing to do before putting everything in the trash.