Camry only clicks
 

I just replaced the spark plugs in my 1998 Camry. I have checked and double checked anything I disconnected or even moved. I turn the ignition key, and all it does is click. Under the hood, it sounds like the battery/starter area. A new starter was installed three weeks ago. The battery is fully charged; it does not sound like a battery problem. The click happens once. Turn the key off, turn it to start again, and it clicks once. Anyone have any ideas?
Thanks.

Typically this issue would be caused by a bad starter solenoid. Is the starter new or rebuilt? If a rebuilt it can have issues right out of the box.

The starter solenoid and starter are bolted together. There is a large electrical cable going from the solenoid to the starter. This ign key powers the solenoid which closes a switch that connects battery power to the starter motor.

Check the following:

Problem battery cable terminal connections at the battery.

Problem battery terminal connections to the battery cables themselves.

Problem negative battery cable to chassis ground and ground point.

Bad battery to starter solenoid cable. The cable can fail and result in not enough current flow to the solenoid. The cable will still have voltage at the solenoid. This cable can be bypassed using a jumper cable.

Can also if careful momentary touch one end of this jumper cable directly to the starter motor electrical cable terminal connection. This will bypass the starter solenoid.

Obtain a section of electrical wire. Jump the ign key system by momentary connecting this wire between the battery cable terminal at the solenoid and a SMALL wire that also connects to the solenoid. This SMALL wire typically has a push on electrical connection. This action will bypass the ign key.

In this order the problem is typically a bad solenoid, electrical connections at battery, battery cable to starter solenoid, negative ground issues, ign key issue.

Had the same problem with my sons 1998 Camry and I was convinced that the clicking was coming from a bad starter/solenoid. After fiddling for over an hour decided to try using booster cables from my car and it turned over and started straight away. Didn't I feel stupid.

Sohoman has a good point. Try to rule out the battery first. When you turn the key, make sure someone has a volt-meter on the battery terminals. if it drops below about 8-volts, it may not turn the engine. Most cars on a good battery won't go below about 10.5 volts during cranking. You can buy a basic voltmeter for less then or about $10-. If your battery is good, then follow with the other suggestions made above.