well first you need to learn 1 important fact about midi:
midi involves data only, not sound (unless you have a pair of midi headphones), so basically... your korg (korg what?) being attached to the mpd using midi cables is just so you can record key presses and play them back. you still need the audio outputs from the "korg" to be plugged in to the mixer etc...
try this:
attach a midi cable from the mpc midi output A to the input on the korg, and then attach another midi cable from your korg midi output to the mpc midi input 1. now in the mpc midi options set the midi out to channel 1, and do the same in the korg...
see what that does. if that doesn't help, then RTMFM of both pieces of gear. (yes the manuals are available on the official websites of the companies.
MPC-Live/Remix16