Why did America ban new cars and set the speed limit to 35 mph in 1942?

They didn't ban new cars. The car manufactures stopped producing cars and switched to building military vehicles and weapons for their part in the war effort. Oldsmobile, as an example, built their last vehicle for the public on 2/5/1942 and resumed production on 10/15/1945. Between those dates they built military items for WWII.