Can you help me troubleshoot a squeaking refrigerator?

Question

It's driving us nuts! It's not anything mechanical. We can give it a gentle push and the whole thing will squeak. It happens when we open the door, and when it closes, too. It's not a hinge. It's almost as if some interior panel is rubbing against and external panel. We made sure it's not touching the walls, or the baseboard. We made sure the electrical cord is not rubbing on the back of the unit. We re-adjusted the leveling feet. Nothing has helped. It's a Whirlpool, freezer on the bottom, about 6 yrs. old. Any ideas?