When I try to start my Camry it makes a clicking sound and won't start. The lights come on while I try to start it. I'm thinking it might be the battery, but I'm not 100% sure. I had a problem with this a few weeks ago, but it started up about 20 minutes later.

Could it be something else besides the battery?

 

It could be the battery, or the starter, or even the alternator..

 

Typically problems are corrosion or poor electrical contact at the battery cable terminals connected to the battery (clean battery cable connections at battery) or the starter solenoid.

Over time the electrical switch contacts inside the starter solenoid housing burn from arcing during usage and make intermediate or poor electrical contact. Clicking is a sign of this problem.

These contacts can be replaced without taking the starter motor/solenoid off the engine. Check with the dealer for replacement parts.

An internet search on "replacing the solenoid contacts" plus your engine model should produce hits on this issue. The 4 cylinder model is 5SFE, the V6 is 1MZFE.

Clean terminals first. Then check the solenoid.

Note: If the original starter is a Toyota brand and it is the solenoid contacts suggest repairing rather then buying a rebuilt at parts store. You will save money plus the Toyota brand starter is a quality part unlike what you might end up with from a parts store.