It looks like your laptop drive has a proprietary connection on the back of it, you should be able to take those two screw out and remove that piece. It should then fit on the sata side of that connector.
Actually in looking closer at the drive, it looks like there is a casing around the entire drive which will need to come off, and is probably holding the part on the back in place. The sort of metal cradle the drive is sitting in is the part i'm talking about. Compare your drive to this one, and notice how your's has the extra casing around it.
I'm new here but thought I could shed some light on this USB cable of yours. This only provides the data cable for your HDD, but does not provide power also. What you would need to do is find a Desktop computer with a SATA power cable, (most modern computers have them) Connect the hard drive up to the SATA power cable (WITH THE POWER OFF!) then plug your usb in, connect a SATA cable upto the usb adapter then put it in the hard drive.
This should now hopefully read your hard drive. (if you need the usb......) if not skip this part.
Onto the next problem... If the hard drive is showing as blank or not showing data, you may wish to consider running the CHKDSK function by going to run (Start button and press the R key) - type 'cmd' without the quotes.
Now the black windows is up type this: 'chkdsk /f /r C:' - or which ever your hard drive is at the moment... F: for example.
Restart, then let it do its thing,
If that don't work... then I'd try going into My Computer, finding your drive (right click) then Properties, then click tools tab at the top, and you should see 'Error-checking' - so click 'Check Now...'
Tick the following::: 'Automatically fix file system errors' and 'Scan for and attempt recovery of bad sectors'
Hope this fixes your problem, if not you'll need to download some data recovery software