Toyota Repair: 96 Camry Starter, starter solenoid, load tester

Question
I checked the battery and it is putting out 14.1 volts. Went ahead and installed a new starter and have the same issue. When I turn the key I get a rapid solenoid clicking noise.

Is there another solenoid between the battery and starter?

Thanks




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Followup To
Question -
Daughter's 96 Camry, 4 cylinder having starting problems. Read several of your other response and it sounds like the starter solenoid contacts. When the key is turned get a rapid clicking noise and the start will intermitently engage. Has gotten to teh point where it just has the rapid clicking. The battery is fully charged and in good shape.

Am I right to conclude starter solenoid problem. If so, is it a pretty straight forward repair to replace  the soleniod contacts. I am assuming there is no magic in removing the starter.

Thanks
Answer -
The rapid clicking noise when holding the key in the start position is normally because the battery is discharged, make absolutely sure that the battery is good and the connections are good before repairing the starter.

Answer
Did you check the battery with the engine running?
The correct way to test the battery is with a load tester which puts an amperage draw on the battery while the voltage is monitored, I suggest you have the battery tested this way, some autoparts stores will do this for you at no charge.