What type of connector is this? (bridges two boards by means of a row of rigid, uninsulated wires)
I have also seen an occasional similar connection. Those are exposed leads, so you will want to keep them straight and not touch each other (of course).

You may have to carefully remove both (or all of the connected) boards at the same time, as the "ribbon" was probably soldered in before the PCB's were installed into the chassis at the plant. This is why many of the small time shops may not even want to tackle this kind of repair.

Good luck though, and a worthy project.