If you have already replaced the battery, then you have a few other things to look at.
- It could be the starter itself
- it could be the starter solenoid which might be integrated with the starter or mounted somewhere in the engine compartment. You can find it by tracing the thick positive wire (red - about the size of a finger) to where it goes. If it goes directly to the starter then the solenoid is integrated and more difficult to test
- It could be the positive wire itself and is not making a good connection to the battery or starter/starter solenoid
- It could also be the ground wire (Black - about the size of a finger). If this wire is not making a good connection from the battery to the engine block, it will keep the starter from working
I would start with the wires, making sure you have a good connection and then work your way to the starter. The clicking is usually a result of the starter not getting enough current to crank the engine.
