After sitting for two months the battery has drained?

When I entered the car to install a web cam, all the lights were on, and I did not notice that all the car lights were on. Since the car wasn't driven in 2 months the battery is probably dead right? Well, the whole car is dead and is stuck in the garage. The lights are all off and the remote for the car doesn't work. Which means I can't lock my car. The car is a push to start and when I press the button it doesn't show anything on the dash.

The is a pretty modern car so would changing the battery straight up damage the computer system of the car?
(The battery has been dead for at least 4 days)

Can I still follow your video (How to replace a car battery and keep the computer's memory-posted 3 years ago) steps to replace the battery by plugging in a portable jumper to the cigarette lighter? (I ask because I assume the car in the Mercedes battery was still working and the battery I have in the car is dead)

Thank you!