The connector on the PCB is called a ZIF (zero insertion force) connector. Normally they are specified by the number of pins, the pitch of the pins, and whether there is any locking feature or "ear" on the sides of the ribbon cable. It looks like a standard latching connector made by any number of companies.
The ribbon cable looks like it is custom designed for the display's electrical pin out and the mechanical design of the enclosure.
If you can figure out the mfg of the display itself, you should be able to figure out the ribbon cable pinout.
I know a fair bit about connectors and circuit fab, but not an EE so hopefully this helps!