2004 solara wont start has a new batterie new starter lights are good

Voltage drop test starter circuit , instead of replacing parts test ! Using a volt meter an checking voltage at certain spots ! An looking at wiring diagram for the circuit in question ! You could have bad battery cables or battery connections , bad starter relay ,ignition switch an so on ! Starter Voltage Drop

This procedure usually works:
·Check the battery cable connections:
Make sure the negative cable makes a good ground connection at the battery and (preferably) at the engine. Make sure the positive cable, makes a good connection at the battery and at the starter.

·Check the battery the simple way, like this:
Turn on the headlights, then try to start the car.If the headlights do not dim or go out, then the battery is likely ok.

·Check the starter and solenoid:
If the wiring looks ok, then look at the starter solenoid for a good connection, and proper voltage at the starter(10 volts minimum while cranking).
If the starter spins and no crank, the problem is most likely the Solenoid's pinion gear is stuck.
Have someone hit (not too hard) the starter while you try to start the car. This usually works by dislodging a stuck pinion gear.
·Make a simple test of the alternator:
If you can, somehow get the engine running, measure the voltage at the battery. It should be at least 13.6 volts to properly charge the battery.

Possibly a bad alternator. No Start Diagnostic Basics EricTheCarGuy