If I remember correctly
The TDS1kB display uses a different cable to connect (the connector on the main board side is larger), and it also connects directly to the PSU for its backlight power (the HV inverter for the fluorescent bulb is on the PSU).
The TDS1kC display connects straight to the main board (I believe the newer displays use LEDs so no need for HV inverter) for its backlight power and the main board connector is smaller.
I don't know if it's a simple pin-to-pin for the display connection, but the power connection should be simple enough. As far as the FW goes, I couldn't tell you.