New battery, new starter just installed wont turn over.

Check the starter, check the cable that goes from the battery to the starter. make sure its tight and not loose. take a hammer and tap on the starter. If the vehicle still doesn't start. Change the starter.

When key is turned the starter is energized by a solenoid that applies power directly from the battery to the starter. Any loose connection will prevent the starter from turning over. The solenoid can also have burnt spots on the contacts inside case that will prevent current from getting to the starter. A click noise is the solenoid energizing so
if all connections are tight and the battery is good the only
other problem is the starter may be bad. Brushes on the
starter may have seen their life ended. this is usually identified by tapping on starter with a hammer while trying to start engine. If starter spins, replacement is needed.

Check the fuse box directly behind battery. Also check that the starter positive is not touching the body

try the starter solenoid or the starter relay....be sure all the starter/ignition fuses are good

this sounds more like the switch is at fault to me if one key will start it and the other wont? its got to be the switch,,,

LOAD TEST THE BAT.NEED 700 CCA.SOUNDS LIKE A NEW DEAD BAT ..THE SOUND IS THE SOLINOID NOT GETTING ENOUGH VOLTAGE.

check the nuetral safety switch and the ignition switch under the column not the key tumbler assembly

Check and make sure you are getting power to the ignition switch and to the stator wire on the starter. Turn the key on and and measure the volts going to the starter on both wires. You should a atleast 12 volts going to the stator wire and to the main wire from the battery. If you are not getting power there it could be a fuseable link in the power wire from the ignition. I noticed that you replaced the ignition switch make sure the rod from the key switch has not come out of the switch.

You will have to check, at the starter, for power to the SMALL wire on the starter solenoid (which is on the starter) when turning the ignition switch to start.
If there is power to this wire ( usually purple ) and power at the LARGE cable ( from the battery ) at the starter end.....you need a starter.

If you do not have power at the small wire at the solenoid with the key in start position and battery power is OK.....check the safety neutral switch.Moving the shifter around a little can sometimes allow the car to start if the neutral switch is worn.

A new battery does not always mean a fully charged battery.
Try a boost from another car before testing the starter for power.

The battery cables need to be clean and tight....and check the ground to the engine as well.

Everything else may work OK with bad connections,they don't use the power the starter needs to turn the engine over.

Sounds like you have a bad starter. To check this you can try taking a hammer to the starter and tap it while someone in the car turns the key. If it starts you know you have a bad starter and need to replace it. Hope this helps you out