Deactivate Photoshop when Computer is not accessable

Hello!
I have a student license for Photoshop from 2013 and I used the programm on 2 computers.
One is broken and I want to move Photoshop to my new one. I deinstalled PS on the old one without knowing I had to deactivate it first. Now I don't have a chance to deactivate it.
I tried to re-install PS on the original old computer, but the programm doesn't recognice the computer and thinks it's another one. So I'm facing the same problem still.
Adobe support couldn't help me, because the license isn't connected to an account.

How can I deactivate Photoshop on my old PC and use the serialnummer again?

Any help with this is highly appreciated!!

My best,
Anna