1989 Toyota Corolla COOLING SYSTEM DOES NOT WORK

Overheating problem relates to 2 things that is an airflow or circulation problem. Lets try doing this 1st before going deep6 on it.

Try bleeding it see below

Always bleed air from cooling system after replacing coolant. Set heater for maximum heat. Remove radiator cap. Loosen drain plug and remove drain bolt (if equipped) from engine block. Drain coolant reservoir. Fill coolant reservoir to MAX mark with 50/50 water-coolant mixture. Loosen bleed bolt and fill radiator up to base of filler neck. Close bleed bolt when coolant flows out without bubbles. Tighten bleed bolt. With radiator cap removed, start and operate engine to normal operating temperature. Add coolant if necessary and check for leaks.

The electric fan should be coming On-if not could be the temperature gauge switch or the coolant temperature sensor when use by the computer to energize the fan relay and then to the fan.

Try direct power to the fan-see if it will operate-

See illustration below

Temperature switch

Coolant temperature sensor