Unlikely. The flat cable is probably connected to the switches directly. You would need a microcontroller.
If there are two (or more) unused lines in the cable, you could connect it to a Teensy 2.0 microcontroller card which has 25 I/O lines, otherwise you would best use a Teensy++ 2.0 which has more. Those have a USB mini-B port and a AVR-family microcontroller. Download source code and build environment for some firmware for AVR, reverse-engineer the keyboard matrix and program a specialisation of the firmware for your keyboard. (there are a few already in a subdirectory).
You are far from the first person to do something like this with an old keyboard from a laptop or electronic typewriter. TMK and QMK are the most popular firmwares. I think there is one made especially for old keyboards that can learn the matrix by "typing" instructions and asking you to press each key in turn but I don't remember which one that was...
