You could call the owner, tell them to set it to heat, turn the temp way up and see if the furnace/blower come on. If so, then you have power to the inside unit. Outside compressor will be on a separate breaker. They have an access cover, you could look for 24V on the low voltage wires to the contactor, but be careful, you have 240V nearby.
One thing not mentioned was a float switch in the new setup, so I take that to mean there isn't one. I suppose there could have been one in the old pan and whoever replaced it disconnected it and left it open. That would certainly keep it from running. I think it's probably wired in series with the thermostat wires, not on separate wiring. Who did this work? If it was an HVAC pro, 99% they would have tested it running. If it's some handyman type, they might not have.
Beyond that, it's a matter of tracing wires and checking for voltage. Should be
24V between the cooling call wire and common at the unit. Cooling is typically yellow. That's what it takes to get the blower running and then there should be 24V on the wires going to the contactor/relay on the outside unit.