If your battery is new and fully charged, a clicking sound usually points to:
Faulty starter solenoid
Worn starter motor brushes
Poor ground connection
Try this test:
Tap the starter lightly with a tool while someone turns the key.
If it starts, the internal brushes are likely worn.
Most Corolla starters last around 150,000–200,000 km, so replacement is common at higher mileage.