Anytime I deal with service personnel there's always a work order and an invoice involved. That way we both know exactly what is being done and what the charge is. Her attitude was most uncouth, no doubt, but two weeks is an awful long time to wait before collecting.
Maybe she was mentally ill and honestly didn't remember you? Though honestly, if someone showed up randomly to collect money from me and I didn't immediately recognize them I'd probably freak out a bit, too. That probably goes doubly for a woman.
As for the new unit waiting to be installed, perhaps the old one tanked in the time between your visits. Stranger things have happened.
To conclude: You should probably not do work if the person paying isn't on hand. AC is super nice, but like Rich said in most places it's not necessary for survival, the exceptions being old folks in the warmer regions like Arizona, Texas, and possibly Florida.
Eww, cash. Always freaks me out when people want change. Pizza delivery was way too strenuous back before the card days.