Hello, I am Randall. I have reviewed your question and working on it now.
Since new battery, all works. nothing with key? I really have to lean to a fialed starter. be sure you are trying to crank it in neutral as well just to be sure the park switch is ok
If no crank in either park or neutral, I highly suspect starter is bad
If you remove the air box as shown below, the starter is down under that on side of engine
If you locate the purple wire, have someone turn and hold key to "Crank" you should have power, 12 volts on the purple wire at the starter, If you do? I i suspect you do? then starter is likely the problem
You can then.. try hitting on the body of the starter with anything you have to hit on it hard as sometimes this will unsick a bad starter, no promise but is siomething done and tried
I hope this helps. please remember to rate my service before exiting the site so I can be credited for my time.
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