Since both front and rear a/c units are not cooling that gives you a direction to head in.
A/C units have a high and low pressure switch to protect the system. If you had a set of gauges you could read the high and low pressures which would give you an idea of what is going on. The usual problem is a lack of refrigerant due to a leaking seal or a hole in the components. That will trip the low pressure switch and give the impression that the compressor is cycling.
Another problem can occur when the compressor craps out, plugs the orifice tube then trips the high pressure switch due to the blockage.
When the system is running, does the a/c line the goes to the accumulator get cold? Or if it is easier for you, does the accumulator get cold?