09 iMac hard drive crash, can new macbook recover files?

So I happily owned an iMac (Sept. 2009 model) for many years. The hard drive began a 2 day process of suddenly failing which I believe is a physical problem from the sound and some other diagnostic tools. I do know it still spins for the purposes of extraction. I already took it into an apple store, and tried all of the simple things you do at the beginning. Apple could not get into it to reinstall the operating system because I had it password protected and we can not even get to that screen.

What I heard was that there was a way to at least use some kind of affordable, free, or preinstalled loop hole program with one of the non-USB ports and a cable (i.e. lightning) to transfer my old files onto my newer macbook pro.

Has anyone else heard of this, or have a good fix? It would be good to get some of my documents and family pictures back.

Peace and love to everyone, but let us not go anywhere near the issue of "why didn't I have an external back up?" or comments that don't help. Long story, I moved it around in the army, part of what I think caused the physical damage to the HD.

Thanks Community

Ced.