Actually, it sounds as if the charge is low, and that would cause all the symptoms you're talking about.

-fast cycling
-auxiliary fan won't come on
-poor output

In fact, before you even bother chasing electrical gremlins, find out if the charge level is correct. Then determine if the electrical system is not performing. The root cause it probably the charge level. The auxiliary fan won't work without a certain level of high side pressure, which by the sounds of it, isn't present. A low pressure side gauge will tell you if the compressor is cycling off at a certain pressure, or just cycling off randomly. You'll find that it is probably just shutting off once it reaches it's shutoff point. When the charge is low, this will happen very rapidly. In fact, if the system is full of R134a, at low temps, the A/C may never even activate at all.

I highly suspect that the only issue is the charge level, and once corrected, the other symptoms will disappear as well.

Could be a clogged expansion valve or some other restriction in the high side connections. Causes pressure to build up rapidly on the high side, tripping compressor, but freon won't go through the clog so no cooling. If you put gauges on the system, you should be able to see it happening.

Short cycling of the compressor is the classic symptom of low freon. Not sure but on your car the aux fan is controlled by a high side pressure sensing switch not the dash AC controls. Therefore if pressure never builds the fan will not come on.
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David Hunter