Selector feel has zero to do with battery. In my 2013, after having the battery disconnected, when starting for the first time there’s a 50% chance of it turning off. It feels like the ECU or TB is learning.

I’d suggest getting a volt meter and checking your new battery’s voltage. Make sure battery has over 12V first. Preferably closer to 12.3 as a minimum. Assuming it does, then it should crank. But prior to first start put key in ON position and wait about 30 seconds. You’ll hear the TB opening and closing.

Let us know the voltage.

Also once it starts check voltage again and make sure the alternator is charging.