OK, this all depends on how skilled you are:
Easy Method:
1. Insert the ribbon back into the slot.
2. Take the broken part of the clip and lay it back down right on top of the pins. If you don't have the black switch then simply use something like a very small flat head screw driver or a needle instead.
3. Put a bit of pressure on the pins then lay a good sized piece of black tape or even glue gun glue on the area.
Skilled Method:
1. Remove any covering on the connector area revealing the bare pins.
2. Either you lay the ribbon on top of the bare pins and glue gun or black tape the ribbon to the pins while asserting pressure, OR use thin wire and soldier the pins to the corresponding contacts on the ribbon, then clean everything up with glue gun or black tape. Make sure the wires don't touch each other.
Either way, the ZIF connector that you broke is the one to the backlight for the LCD of the Gamepad. Basically this component gives the screen light. This repair could be done the same way to any ZIF connector so if you break the digitizer one next, you can fix it the same way.
Take your time next time, your welcome!