I went through something similar to this with my Rheem gas furnace/central air system a few months back. In short, check the resistance of the AC power contactor primary side (where the 24 V AC connects) inside the AC unit. If the resistance is outside of specified resistance range by even a few tenths of an ohm, the contactor is likely bad and will need to be replaced.
The 24 V AC from the transformer is used to power the control circuits in your system - thermostat, relays, contactors, etc., and if something pulls too much current through the 24 V AC transformer, the primary of the 24 V AC transformer will open like a fuse killing the system. No fan for the furnace, no power to the thermostat, no "low voltage low current" to operate the main power contactor in the AC unit.
I was told that in older, say over 12 years old, Rheem/Rudd systems, the 24 V AC transformer was used as a sacrificial fuse to protect the AC unit when the AC's contactor went bad. Newer systems and current OEM replacement transformers use a 1 or 2 amp fuse inline with the 24 VAC transformer's primary circuit rather than sacrificing the transformer.
Hope this helps.