Intermittent not starting issue?

My son has the car listed above SXT with a little over 113,000 miles.

One day last week the car wouldn't start. No check engine light or codes. Battery was purchased 3 months ago. Had it towed to a very reputable local garage.

They ran tests. Said the battery and alternator were fine. Couldn't find any problem. My son picked the car up on a Thursday and it started fine.

The car ran fine and started fine the next three days. No problem. Tonight, Sunday, he starts it up, turns it off to go back in the house, tries to start it again, and nothing. No dome light, no dashboard lights. Nothing.

I go to jump the car. As soon as I hook up the negative jumper cable to his battery's negative post, his dome light comes on. I had not hooked it to my car's battery yet. Took the cable off the post and the dome light went off.

Completely hooked up jumper cables, started my car and let it run for about 10 minutes. Unhooked cables and tried to start his car and nothing. Put cables back on, tried to start his car, and it started right up.

We let his car run about 5 minutes after taking the cables off. Lights worked, everything seemed fine. Turned his car off, lights stayed on. He tried starting his car and the lights died and it wouldn't start.

The only other thing to add is that the car is a push button start. Maybe a week before it first died, we had the opposite problem, and it wouldn't shut off. The shifter was in park and the emergency brake was engaged, but a message on the dash screen would say it wasn't in park. After shifting into and out of park several times this stopped. It hasn't happened again, but now we're having the starting problem.

Also, I did notice some corrosion on the positive post, which I thought was odd for a 3 month old battery.

Help.