At times our son's car ('98 Toyota Avalon) does not work and then it will start working again.

Bad brake master cylinder?

Bad power brake booster?

I would go over the complete braking system. Look for leaks associated with the calipers, wheel cylinders, hoses, and master cylinder. Make repairs and then completely change the brake fluid.

I would look at the ABS controller, my experience with toyotas is when the ABS goes out you loose most of your braking ability due to the disigne of the ABS controller.