Accessing internal drive resources from external drive OS

Hi!

I have a situation:

I was working on a large file. Eventually, I had like 20mb or less of free space. The laptop went down and now, after a apple logo at boot, it shows the stop sign. I had it fixed at a service but it happened again. I'm abroad without access to any specialist here. I have another, brand new Pro on me and a 2TB ext drive.

I tried booting it from ext. drive with a system on it, but it just launched installation process, created profile and I couldn't find the internal drive access anywhere.

I tried booting with cmd+r, but there's no repair option. I reset the NVRAM too. I can't go into safe mode- it dies after loading for a while.

Its MacBook Pro (13-inch, Mid 2012)

500GB, 8GB RAM

Please advice is theres anything I can do here to make it work. Client is waiting for laptop's contents and I'm going nuts.