You sure its the starter?
Reason i ask is that i had an auto once, not a celica
but it did the same thing and it was a sensor that had failed, which made it think that the car was in drive and therefore wouldnt start - i'm pretty sure it made the same clicking noise as you describe
Before it failed completely it would do this and if i moved the shift up and down from park to drive and back a couple or so times it would fix itself
then i had the sensor on the gearbox removed as it was a pain, just meant that it lost the safety thing of not being able to be started in drive