Nissan Maxima doesn't start - sometimes

Last week rather than shovel my way into the driveway, I ran over snow (turned out to be ice). Shut off car. Came out in one hour. Car would not start. AAA could not start. Towed to shop. Started every time for them. Since then, the car starts 4 times out of 5. It doesn’t turnover - feels like the starter is disabled. I try again and again, and it starts by the 10th time.



Note: When I shift into reverse, it seems like it doesn’t engage as cleanly as it did before.



Thanks

Maybe your ignition switch (where you put the key) is failing.