Thermostat AC Compressor will not turn on

Thank you.

Easiest for testing is just to bypass thermostat and make connections directly on the contact field on the furnace. Black to Yellow should start A/C, circulator fan, etc. Blower door switch on furnace needs to be held in of course.
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Black to anything will not start anything.
Colors aren’t actually standardized enough to tell people to jump a specific color without knowing what type of system they have / where their wires are currently connected to. Blue is often used as common, unless you have no yellow wire, in which case it is Y, or if you have a heat pump and no orange wire, in which case it is the reversing valve. Of course, I’ve also seen a R wire that was blue, so you really cannot go by color alone.
Black is C on your diagram, which would do absolutely nothing when connected to any other thermostat wire, as all the other loads are already connected to C. The loads all need R switched to them, preferably through a fuse, in case you short something out, or the devices themselves have a short.

OK, then just look up the connection field on the furnace, look up the furnace manual for the actual wiring and “close” the “call” for cooling.

Color coding might not be consistent, but the lettering should. And you are correct, my bad, R is the one that should be connected to Y.