One thing to watch for with the remote is the pre-conditioning will NOT activate if a door is open. Make sure all the doors and rear hatch are fully closed (confirm by pressing LOCK on the remote, good to go if the lights flash).
On 120 volts, the proper procedure is to hold the power button on the remote to wake it up (top button on right side). Press Mode (middle right button) twice to get to pre-conditioning, use the front left/right buttons to select desired mode, and then press/release power button again to send command. The remote should ascending chime 3-4 tones, flashing the antenna icon on the screen for a second or two, and then play 3-4 descending chimes to confirm pre-con is active. The car should then activate the EVSE and start conditioning the car (easiest to try with either the COOL or Defrost options as it will light up the buttons on the center stack).
Just to confirm, does your charging cord say "Mitsubishi Innovative Electric Vehicle" on the face of the brick? Simply turning the remote on will cause the Charge light to come on for about 15 seconds even if no settings are changed when the car is fully charged but still plugged in.