Lexus IS250 2008 won't start

Today, I tried to sell my Lexus IS250 2008. I turned the car on and drove to meet the guy. When I got there I let car on idling because I wanted it to warm up (heating was on, seat heating was on, etc.). I talked to him and he looked at the car for around 15 minutes. When I wanted to leave, the steering wheel was very heavy and brake paddle is very stiff. I turned the car off, but it won’t start on. The first time, I jump start the car, and it turned on. I went to talk with a guy for 2 minutes, then I came back but the steering wheel was very heavy. I turned it off, and jumped started it again. The steering wheel was light, and I drove back home.

What is the problem? Is it the alternator or the battery?