Why is my 1989 Toyota Corolla not circulating the antifreeze?

You have a pump where there hoses attach from the radiator this pump circulates the antifreeze thru the system it this doesn't turn it will cause the car to overheat....I'm assuming the cooling fan are on when the car is up to running temperature

Would it show that it is overheating on my dash? Never had a problem with it overheating before but I'll definitely check it out. Thanks! Anything else would be greatly appreciated as well.

It should indicate over heating as the car is running do you have a gauge or a dummie light?

An '89 Corolla has a gauge. All trims do. Since eddydoes42 didn't answer you joemom, just for information.. Now Cameron if it is overheating it will 'tell'... unless the gauge or sending unit has failed. Check that your reservoir is not over full. It should only be about ¼ full cold. Even empty is OK when cold. But if you filled the reservoir to the brim cold, that will happen. The radiator will form a vacuum as it cools, and suck the coolant back in. But with an overfilled reservoir, when the car gets to normal operating temperature, the coolant has nowhere else to go . In my Corolla the fan seldom even runs, except with A/C on. The airflow at speeds as low as 35 mph or so is enough to make the fan redundant, so no reason to power it up. The 1.8L 1ZZ FE only has one sender, for both gauge and engine fan.

Just to add... I don't know if I am addressing eddydoes42 or Cameron.. get a new radiator cap. If it got so hot and didn't release pressure and actually cracked the radiator... that was the reason. I sincerely hope you didn't get 'taken' by some not-so-reputable shop. The hoses will blow out long before a radiator will crack

plugged radiator