Why do think its a relay??
if it is a single click or sometimes no click noise when turning the key it is the starter itself.
If it is a repetitive click it could only be the battery.
If you hear a click, this is the relay you are asking about, however it is extremely rare for a Toyota.
Please have someone help you with the next step. Get a long metal rod or long pry bar about 2' long and a hammer.
Locate the starter, it will be on the driver side of a left hand drive vehicle between the engine and the transmission.
Set one end of the rod on the body of the starter and tap the other end firmly with the hammer. You don't have to kill it. At the same time as you do this, your helper will be in the car holding the key in the fully start position, don't touch the gas as it may flood the motor.
in mant cases this may start the car.
If you live in a cold climate where they use salt on the roads, there is a small chance there could be a bad ground to the starter but only a 2% chance of this.
of you are handy and can remove the starter yourself, you should check the starter contacts inside the starter.
these copper contacts are usually the only thing that wear on a Toyota reduction type starter. And are not vert difficult to replace if you are comfortable with this level of technical expertise.
Or you can order a new starter from your Toyota dealer as you already know the last one was good for 11 years and they usually have a less expensive rebuilt starter available for your corolla.
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