AC compressor does not engage

What are the operating pressures in the system? To see if it even has any r134A in it toss a gauge set on it. If it has any in it you should see a pressure close to the air temperature in Fahrenheit. If you are sure it has a good charge and the compressor is not coming on, you could jump twelve volts to the positive side and see if it engages and cools.
Here are the relays, diodes. The clutch fuse is fuse 20, the main HVAC control fuse is fuse 36 both in the dash fuse panel.

96 low and 195 high without the compressor running are not correct. With no compressor operation the system should stabilize to a pressure almost equal to the outside ambient temperature in degrees Fahrenheit. So if you have a 95 degree day and the compressor is not working you should see a resting pressure of 95-98 psi on both high and low sides.

If you put twelve volts to the red/white wire and got no clutch engagement then the clutch is bad. It has a replaceable coil that is easy to remove and replace.
The other two wires are the thermal switch that opens if the compressor gets hot.

I suspect you have two issues, the odd pressures suggest a bad expansion valve that is stuck/plugged and the bad clutch.
Once the clutch coil is replaced and the compressor is working you can watch the pressures to see if the expansion valve is bad.

Good call, here is a guide that will help

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

Here is another guide that can help.

https://www.2carpros.com/articles/car-air-conditioner-not-working-or-is-weak

Please let us know what happens.

Cheers, Ken

OK if the compressor came on then it may not be a bad clutch. It does show that the PCM is able to activate the clutch relay so the control side is likely OK.
110 low/108 high would be about 105 degrees F for air temperature. And it should mean enough 134A for the switches to work.
At this point I would probably recover the 134a in the system. Change the expansion valve. Recharge it with the amount on the compressor tag and then check for operation.

Sounds about like my vehicles. Replace one part and the rest get jealous. No rush, we'll be here.

Pressures sound about right for 70 degrees or so. The fan not coming on is an issue though. When it hit's 225 or so the AC pressure switch should tell the PCM to kick the fans to high speed. As neither is turning on I would suspect the pressure sensor. It should have ground to the black wire, reference voltage to the red wire and the signal comes out the green wire. It's possible a bad connection or bad sensor.

Yep, it is down in front by the compressor, here is a diagram that shows its location. (Below)

I believe so, here is a full wiring diagram of the system to help you with the testing. (Below)

Red should have 5 volts reference voltage on it. The black wire is ground. So if you put a voltmeter on them with the key on and AC switched on you should see 5 volts.

To check the signal output measure the voltage on the green wire. With the AC on and high pressure below 212 psi. You should see.7 to 1.94 volts. With high pressure over 213 psi you should see a voltage from 1.95 volts up to 4.5 volts.

If the above check out then you will need to check the control signals out of the PCM to the fan relay.

The switch will cut the AC off at 4.5 volts which is around the 450 psi mark. So I would say the sensor is OK. That signal feeds into the pcm and it determines the fans speeds and running condition. The PCM then turns on one or both fans as needed.

You wrote that before the starter died you replaced the relay and the fan worked for a bit correct? Then it stopped working. If that is correct I would really check that relay socket. A loose pin might account for the problems. I would also check the signal right at the PCM for both the sensor and the relay.