Transformers often do make noises like buzzing. So don't worry.
I hope when she decided to replace the thermostat, she turned off the power. You may want to ask her.
Your first task is turn off the power. Go to the air handler and make note of the color of each wire, that is now disconnected, at the control board.
Now go to the thermostat and remove the cover. Verify you have the same number and color of wires connected there as at the air handler. That will almost guarantee no one has spliced any new wiring.
Now carefully read the thermostat installation instructions for a heat pump paying close attention to the setup section. Make sure she has it wired correctly.This step is critical.
Now make a list of the wire color and to which terminal on the thermostat it is connected... like Red wire--- R terminal.
Once you have this map, go to the air handler and reconnect the wires following the map you just made.
Turn on the power, say a few chants to whatever deity you like and see if it works.