Why doesn't MacBook Pro recognize hard drives in recovery mode?

Question

macbook

While working, my MacBook Pro (2012) froze for a long time, I had to force shutdown, after which it would not start again. A folder with a question mark flashed.
I connected TimeMachine, a section with utilities appeared, opened disk check, MacBook recognized only TimeMachine.

Because My wife and I have two MacBook Pro 13's (mine '12 and her '10) so I decided to try this:
Plugged the hard drive from her computer into mine, OS X started without any problems. In other words, my MacBook recognized another HDD. So the problem is in my drive ... I connected it to my wife's MacBook and her computer recognizes this drive. In other words, the disk is correct.

I tried to restore a backup from TimeMachine using her computer and put it back in my own, it does not work.
I don't understand what the problem is.

What we have:
MacBook Pro "Core 2 Duo" 2.4 13" Mid-2010 + (HDD Hitachi MLC DA3350 250 GB )
MacBook Pro "Core i7" 2.9 13" Mid-2012 + (HDD WD5000LPVX 500 GB)
And another HDD Hitachi MLC DA5113 750 GB

PS
My MacBook only recognizes HDD Hitachi MLC DA3350 250 GB

Answer 1

In general, this is what happened:
I immediately checked the disks on Mac and Windows, with formatting, they are fully functional and the problem is not in them.
I finally came to this conclusion when I decided to try another option, swap the Hard Drive Cable (HDC). In the MacBook Pro (MBP) 2010, it is slightly thinner and longer than in 2012, but still connects normally, i.e., it is suitable for the test.
Tested on three HDDs in both MacBooks. The motherboard on my MacBook is fine, the HDC from the 2010 MBP connects all drives properly and flawlessly, but the HDC from 2012 on the MBP 2010 failed to connect two of the three.
In general, this is some kind of problem with the HDC of my MBP, that's just why, since it is broken, it still connects one disk (HDD Hitachi MLC DA3350 250 GB) out of three, I have not yet understood.
PS
Because I don’t have a suitable tool, I’ll try to visit the Apple Store in the next port in Hong Kong, I wonder how much it will cost to check and replace the HDC ....
UPD [08/11/2015]:
I visited the Apple Store in Hong Kong, they said that cable replacement will cost 450 HKD ( 58 USD) this is together with the work, they did not sell me a separate cable. But even on ifixit, the cable costs between 35-45USD, and on amazon it’s even cheaper. I will order from somewhere.
UPD [12/14/2015]:
I received a new cable, installed it, all disks work properly. I ordered the cable from Amazon.

Answer 2

There may be a problem in the system board, Try to boot from a USB flash drive with an axis!
and even if it is possible to check the screws on a third-party PC with Windows OS, go through the disks with Victoria

Answer 3

Perhaps not the entire file system survived. That is, the file log may not be damaged, but the boot part has suffered. Try connecting your drive to your wife's computer and use Disk Utility to erase and re-create the partition(s) on your drive.