Yes probably the original. What is the coil resistance of the clutch? Do you see it activating but not enough movement to contact the freewheel to engage?

 

After having a look around the factory service manual I found this information:

• The pressure switch is a dual switch hence the 4 wires: Open with the refrigerant pressure at less than approx. 2.0 kgf/cm2 (28.4 psi, 196.1 kpa) or more than approx. 32.0 kgf/cm2 (455 psi, 3138.1 kpa)
• the coil resisted to the clutch does not seem to be listed in the factory service manual
• I will observe the clutch carefully to see if it actually moves some. I do not hear the characteristic clicking noise of the AC compressor engaging at present

* the low pressure line for the AC system has been replaced by the previous owner, as a now have one that says Goodyear on it, so obviously the system has been drained and refilled at least once.

This video shows replacement of the clutch:

 

Does the A/C work at all? Does it work when the engine is cold, then stops working after it warms up?

 

at the moment the AC does not work at all, although before it stopped working completely, it would occasionally kick on when driving on the highway. If I put the AC on about 15 minutes into my drive it might suddenly kick on. I suspect this indicates that the field coil itself is still good because if it was bad it would never have the chance to work at all and as such I think the vibrations of driving on the road are shaking the compressor enough for the clutch to suddenly kick in


per this video the resistance of the field coil is 3 to 5 ohms.

 

Try carefully tapping the clutch with a hammer when it's running and see if that gets it to engage. I had to do that on my truck to get it moving before I replaced the entire compressor. If it starts moving with a light tap, you should be able to remove a shim and get it engaging again.

 

I tried doing this but nothing happened. I tried lightly poking at it with a crowbar, perhaps I was not applying enough force.

Also, if I look on eBay or Amazon there seem to be plenty of aftermarket air conditioning compressor clutch kits for this car, but I cannot seem to find an OEM grade compressor clutch set anywhere. I was watching a YouTube video where the bearing in the cheap Amazon kit failed and ruined the compressor. I am kind of leaning towards going to the junkyard and finding a low mileage crashed 2008 Corolla and just stripping the clutch set off of it.

 

I removed the clutch plate without actually removing or loosening the AC compressor at all. It also seems that to do the adjustment you do not even need to take off the Serpentine belt although I did do that. The key to getting the compressor clutch plate off is to not pry in the air gap which I did do and cause some damage. The key is to pry at the little gap where the two sections of the clutch plate meat and are riveted together. I also sprayed some WD40 in there. I removed the bolt that holds the clutch plate down using a 10mm socket and a U joint and a very long extension and a little impact gun. When we tightening the bolt I jammed a screwdriver into the aforementioned gap between the two sections of the clutch plate to hold it down while tightening it with a ratchet, using an assistant of course.

After removing the clutch plate I found a single washer under there which I considered standing down power but ultimately just used the washer which is about half its size which I had in my scrap pile.

the AC system is now working again

I also deduced why prying at the air gap is pointless when trying to remove the clutch plate. When prying at the air gap gently, you’re not able to transmit any pressure into the actual shaft to pop the little clutch played off because of the rubber fill in it it has a rubber core separating the two sections of the part just like a crankshaft pulley.

 

I'm glad you got it working. Just trying to understand the sequence you used. The center bolt is removed first before trying to remove the clutch plate, so I hope that's what you did/meant. Spraying any kind of lube in there is not going to help since it won't make it's way to the shaft splines. You don't want to spray or apply lube onto a clutch surface, though. You can use a little bit of anti-seize on the shaft splines if you want. I don't usually find it necessary, though. Another way to remove a stubborn clutch plate is to use whale-jaw vice grips attached to the clutch and then you have something to grab onto both sides to yank it off. Often they slide right off without much fuss.

To answer one of your original questions: I got 185K miles from the original compressor. I used a Denso aftermarket replacement compressor and it has been about 254K additional miles with no issues so far on it. I expect it won't last much longer, but who knows.

Anyway, you got it working, so.......good.