Then one last thing I would check to verify the ground.
Take some jumper cables, connect them to the battery.
Put the neg side to the casing of the starter or a bolt on the starter.
This will ensure a good ground.
Then touch the positive cable to the connector of the starter.
For sure this should make it turn.
Are you absolutely sure your battery is good? Even a bad battery can show 12 volts when there is no load on it.
You can test the battery by turning on your headlights and brakelights and even the horn, they should stay on for several minutes to know that you have a good battery.
Let me know what happens.
Edit: Sorry, I just read your post where you said that you just bought a new battery, so that can't be the problem.
Try running a separate ground to your starter as a last test, but it is looking more like the starter is the problem.
Take some jumper cables, connect them to the battery.
Put the neg side to the casing of the starter or a bolt on the starter.
This will ensure a good ground.
Then touch the positive cable to the connector of the starter.
For sure this should make it turn.
Are you absolutely sure your battery is good? Even a bad battery can show 12 volts when there is no load on it.
You can test the battery by turning on your headlights and brakelights and even the horn, they should stay on for several minutes to know that you have a good battery.
Let me know what happens.
Edit: Sorry, I just read your post where you said that you just bought a new battery, so that can't be the problem.
Try running a separate ground to your starter as a last test, but it is looking more like the starter is the problem.
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