Here's a couple of write-ups on troubleshooting the a/c. Most was written by Mike_c.
A/C diagnostic connector is a small 2-wire connector hanging under the dash. Generally it's taped to the wiring harness behind the stereo:
* Remove the passenger side "knee panel" (under-dash panel); don't bust the sensor clipped to this panel.
* Remove the carpet/trim panel on the side of the stereo console.
Look at the back corner area of that carpet/trim panel for a couple 2-wire connectors - one goes to the sensor on the knee panel; next to is the diagnostic port. It'll have green and black wires.
The glove box connector (where the ECU diagnostic port is) also has a pin for the a/c:
"P" is a spot for a pin - may or may not be used, "k" are the two empty spots that "key" the connector, and "G" is the green diagnostic wire.
Typical a/c problems:
* on the thermostat housing there is a small temp on/off switch; this sensor should read 0 ohms to ground on a cold or warm engine. On an overheating engine it'll read infinite ohms. This sensor fails regularly (infinite ohms) killing the compressor. You can just ground the wire going to it as a test - a yellow+white wire.
* Dual pressure switch - one of the sensors in the refrigerant lines near the receiver/dryer. This thing senses too little refrigerant pressure before letting the compressor run (if the "resting" refrigerant pressure is too low the won't be any oil for the compressor; this switch prevents the compressor from running in that condition). It also senses too much pressure and kills the compressor before a/c hoses explode. It's rare for this switch to fail, you can unplug the connector and jumper the wiring harness though to simulate a normal sensor: green+yellow and green+white wires.
* Inside the evaporator box (under-dash box that actually cools the air) is a temp sensor that the a/c computer uses to prevent freeze-ups. If this sensor reads too much resistance, the computer thinks the air is colder than it really is and the compressor gets turned off. Look for yellow+blue and red+green wires (coming from the big black plastic box; the connector will be near the diagnostic connector actually), unplug the connector. Using an ohmmeter, measure the sensor resistance: it should read about 1000 ohms on an 86 degree day; about 5000 ohms on a 50 degree day. If the resistance is above 5000 ohms the a/c computer will be thinking "very cold air, don't need the compressor."
Have you looked for error codes from the a/c computer - it's in a 2-pin connector in the wire bundle near the stereo & passenger knee panel. It's often confused for the knee panel temp sensor connector by the way; it should have a green and a black wire. If the a/c computer is "happy" you'll have a constantly flashing/blinking 12volts-0volts-12volts cycle. Otherwise it'll spit codes.
I'd also put a voltmeter on the a/c condensor relay coil wires and see if the computer is trying to turn it on at all... lately I've seen a couple that only spit out 3 volts or so... rather than 12. Bad a/c ECU.
Otherwise you've already covered the usual suspects. The a/c ECU, relay, and fuse #7 are about all that is left.
A/C compressor is affected by a couple thermoswitches and the pressure switches:
* the small 1-prong thermoswitch on the thermostat housing itself is the GROUND for the compressor relay. This temp sensor often goes bad. Easy test: disconnect the wire going to it and ground the wire instead. If the compressor runs properly, the sensor is shot. It's supposed to be an on/off switch - not a variable resistance sensor like the sensor feeding the dash temp gauge. On an engine that is NOT overheating, the sensor prong is shorted to ground (so the compressor relay and compressor work normally). On an overheating engine, the sensor "opens" killing the a/c compressor. Usually this sensor rots internally and NEVER completes the ground (often you can rotate the connector tang when this happens) so the a/c compressor never turns ON at all. A rapidly cycling compressor usually isn't caused by this switch - that'd be a funky failure mode for this switch/sensor.
* teeny thermosensor wedged against the evaporator underneath the dash. The a/c computer uses this sensor to monitor the refrigerated air temps; mostly making sure it doesn't get cold enough to start ice formation. Also, when the a/c system is working correctly on AUTO, you'll notice the fan doesn't run at full speed until the air gets cold... this temp sensor feeds the a/c computer that info. To replace this sensor, you have to drain the a/c refrigerant and remove the evaporator box from underneath the dash... not fun. It's resistance CAN be checked though easily; it's a simple two-wire connector coming from the evap box. Unplug the connector and stick an ohmmeter on it. An overcharged system will result in too-cold air temps causing the computer to cycle the compressor more often.
* refrigerant "dual pressure switch" that kills the compressor if the refrigerant pressure is too low (no refrigerant or most has leaked out) or too high (about to burst the a/c hoses because of too much refrigerant, problems with the fans on the front of the car, front radiators blocked with dirt/leaves, etc).
Typical dash vent temps (center vents) are around 50 to 54 degrees on a working R134a converted StarQuest a/c.