Target disk mode problem

Hey everyone!

My GF has a 2012 MbP with a corrupted OS (don't know the exact version) that doesn't boot, and keeps asking to setup a fresh OS installation.

We took the machine to an Apple store, and after running the system checkup, we were informed that the OS was corrupted but the HDD was still okay. There isn't a recent backup, so at this point before reinstalling a new OS, and since the HDD is still okay, we want try to save any relevant data from the HDD.

So we were instructed by the genius how to boot the computer in target disk mode to try at home. I have a 2007 Mbp with 10.11.6, connected the computers via firewire 800, faulty MbP has no problem connecting in target disk mode and on the disk utility the faulty disk is recognised, but then the disk doesn't get mounted.

I've read online that sometimes the target disk mode takes some time to mount, so I left the computers connected for a few hours, and nothing happened. And if I press mount on disk utility, nothing happens as well.

Is there anything else I can try to do?

Thanks!