Camry 1996 starter problem

I have a 96 toyota camry that wont start. when i turn the key, the starter clicks but doesnt turn. I replaced the starter and it works fine (as does the one i took out). the battery was obviously checked and is charged. when i hook up the starter to the leads and its not in the engine it doesnt turn (in other words, its not a locked engine). I replaced one of the fuses in the starting relay and it didnt make a difference. So the problem is between the battery and the starter - the starter isnt getting enough power (if i take it to an autoparts store it works when hooked up to their system but doesnt work (but makes a click) when hooked up to the car. any ideas?

I’m confused. Does the new starter not work in the car?

You say the engine isn’t locked - I take it you mean ‘seized up’. How do you know?
Did you try turning it by hand with a socket on the main pulley to see if it turns?

Get a cheap multimeter and check between the fat lead that goes to the starter and the starter’s ground. You should have 12V there all the time. If you don’t, move the ground to the battery. If you then see 12V, you have a bad ground else that fat lead is bad.
IF you do see 12V and still just hear a click, hit the starter with a hammer and see if it wants to start. If it does, your starter likely has some sort of intermittent issue.

I4 or V6?

Either way, I believe the starter solenoid in this engine is repaceable as a seperate part from the starter motor. Did you replace the entire motor assembly with the solenoid or just the motor?

The solenoid assembly also contains the mechanism to engage the contacts that energize the motor circuit, which is why I ask. Those contacts can get hokey as they wear. When that happens, you’ll hear the clic of the solenoid but the motor circuit won’t be completed and the motor won;t turn, or in some cases the contacts will turn highly resistive, “drop” much of the voltage, and there won;t be enough left for the starter to turn the engine. DC motors’ power levels are directly related to their applied voltage.