I have a Akai
This cable is an interference fit cable, and slots, pushes into a header female clip on the PCB. Cold solder will not work, as you found out. You really need to obtain another cable, and detach it from the other end, and replace it in total.
If that's not possible, then your only other way, would be to obtain some fine wire, a very low power soldering iron, a fibreglass pencil, 7 fine solder. Now you would need to identify, where it connects to, and with very fine wire, run a wire from each, connection on the ribbon cable, and solder it to the corresponding place on the PCB. You use the fiberglass pencil to clean off any coating to expose a solderable surface, on the wires, then quickly attach, the fine wires, then when they are done, use Kapton tape or similar and use that to secure and support, the joins, (Sometimes I use hot glue, and lay it down in a position making sure nothing is touching etc, and apply hot glue in a bead right across the joints and it keeps then in place insulated and isolated. Anyway once you have done that, then you need to solder the other ends of the wire to where they would have gone, on the PCB. again make the connection, and use tape, hot glue whatever, and secure that too. If you are careful & have a good magnifying glass, glasses, and patience it can be done.
As an aside here could you not take the cable off from the other set you have, maybe they are the same? Then you could use that one?
You really need to get what we call a service manual, this has all the parts in exploded diagrams, schematics, circuitry etc They are just invaluable. If you contact Akai, they will provide you with one. I have searched the 'net, but have been unable to find one. In the manual there are parts numbers and descriptions, maybe you would be able to purchase a replacement, if you cannot, make or retro-fit the other one?
