No 4 wheel drive engaging

Typo’s fixed for clarity:

After purchasing 4 new tires at Cosco for my 2002 Ford Explorer we brought the car to a local auto shop for the alignment. The 4X4 was working before we dropped the car off (it was snowing) and was not working when we drove it home.

The lights on the dash do not light when high or low 4x4 buttons are pressed, and we can feel there is no 4 wheel drive engaged. The 4x4 low light shows for a few seconds when turning on ignition.

What might cause this to happen and what diagnostic evaluations should we consider? What is a reasonable repair cost to expect?