Problems with central air conditioning?

This is an apartment. The inside fan motor wasn't spinning, but the outside heat exchanger was working. The unit is in the ceiling of the apartment. I opened up the access panel, and saw that the thing that looks like a radiator was covered with ice. It was melting, and I put a bucket under it. I turned the fan from auto to "on" and the fan came on. I turned the other control from off to "cool" and all I could hear was a click. The outside heat exchanger would not come on. I would flick the 2 switches on and off, and occasionally the outside exchanger would come on, but 98% of the time it just made a loud click. What could be the problem, and how would I diagnose it? I've replaced several faulty motors/capacitors and contactors before on different units. Something like a condensor or compressor is beyond my capability. Right now, the ice is thawing. There is no safety switch that disables the unit when the access panel is removed. Thank you.