Hi Jeff,
To control the Korg with the T4 keyboard you only need ONE MIDI cable, from theT4's MIDI A OUT to the Korg's MIDI IN.
On the T4, go to Function > MIDI and select the Preset MIDI Template "KBD & STYLE". Then close the MIDI display with the EXIT button to save the changed setting.
The "Upper" part (all three Right parts) of the T4 is now sent on MIDI Channel 1, and the "Lower" part (Left part), if enabled, on Channel 2.
On the Korg you have to make sure that the data coming in via MIDI IN on the MIDI channels mentioned controls the desired sounds. I can't help you in detail at the moment, because I haven't dealt with Korg keyboards/synths for a long time.
Hope this helps!
Best regards,
Chris