Most of these are available as machine based exercises, I threw a few smith machine movements in there in case those are fair game for you.
Legs: Leg press, leg extensions, leg curls, calf raises, Squats (smith machine?)
Back: Row, High Row, Low Row, Lat Pulldown, Reverse Flies, Upright rows (smith machine?)
Chest: Bench, Incline Bench, Decline Bench, Flies
Shoulders: Flies, Reverse Flies, Shoulder Press, Military (smith machine?)
I'm sure there are a bunch of others out there and your gym may or may not have that equipment.