If the hinge on your old Macbook Air has cracked--I'm sorry. Replacing the hinge is costly and difficult (prying the glued bezel from the screen).
This instructable shows how to make a brace that will
1) prevent further damage
2) allow continued use of your computer
This will not fix the hinge or allow you to close the machine.
First, print the two end pieces (or have them printed, shouldn't cost more than a few dollars). Get a 24 inch long 1/4 inch x 20 threaded rod (available at Home Depot) and cut to length (about 14 inches).
Place the end pieces on the computer and tighten the threaded rods to hold the assembly together.
Your thin laptop has now become a thin desktop machine, but it is still functional and you can (without panic pressure) determine whether to repair, replace or live with the situation.