If the battery is good, all connections are clean and tight, then it sounds like the starter is bad. However, the clicking still sounds like a weak battery to me or a bad connection.
Keep in mind, the starter places a heavy load on the battery. A weak battery or poor connection will cause problems like this.
Regardless, if you are sure it's good, then you should remove the starter and have it bench tested. Here is a link that explains how to replace a starter. These directions will help you with removal and replacement:
https://www.2carpros.com/articles/how-to-replace-a-starter-motor
Here are the directions specific to your vehicle. The attached pics correlate with the directions.
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2013 Kia Forte L4-2.0L
Repair Procedures
Vehicle Starting and Charging Starting System Starter Motor Service and Repair Removal and Replacement Repair Procedures
REPAIR PROCEDURES
Starter
Removal
1. Disconnect the battery negative cable.
2. Disconnect the starter cable (A) from the B terminal (B) on the solenoid (C), then disconnect the connector (D) from the S terminal (E).
pic 1
3. Remove the 2 bolts holding the starter, then remove the starter (A).
pic 2
4. Installation is the reverse of removal.
5. Connect the battery negative cable to the battery.
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Do me one favor before you remove the starter. Try this test and let me know the results:
https://www.2carpros.com/articles/car-battery-load-test
Let me know.
Joe
Images (Click to make bigger)
Wednesday, June 10th, 2020 AT 8:34 AM