My 01 toyota corolla le radiator fans wont work

There's also a thermoswitch driving the relay, that could be bad.
You could apply 12volts directly to the fan connector to see if it will run.

You could

Using a test light connect the lid to NEGATIVE and start the engine with A/C on.back probe the positive terminal on the fan.If no power test the fuse. if fuse OK switch the relay with the horn relay and test again. if you have a power to the fan connector switch the test light lid to POSITIVE on you battery and test for good ground to the fan.some times ground wire can corrode and create a lot of problems. If you have good Power and Ground replace the fan.
good luck