Air conditioner not working

[Meestahbig]

It's been awhile (2+ years) since my 2003 needed any repairs, but recently a bunch of stuff has gone wrong and I am tackling them - coolant and power steering fluid leaks resolved. Now onto my broken AC.

I've replaced the compressor before in 2016 and it's worked fine until now. I only have brief notes about the swap being pretty straightforward, but forgot a lot of the details.

I do see the belt running when I call for AC, so pretty sure the switch is OK. The system is holding pressure and has a full charge - so I don't think its been leaking bc it is now low.

Here are a few questions:
1) how can I rule out a bad temp switch and bad pressure switch?
2) I forgot how to test the continuity on my existing compressor
3) how to determine my compressor is actually dead and the cause before shelling out $300 on a new one.

Thanks.