No, this isn't directly connected.
"ein Computer" means "a computer", ein also means on. Eingang is something different, which may have been linked in ancient times, but isn't now. Eingang and Ausgang are used as well for "input" and "output" on radio equipment as for "Entrance" and "exit". "Aus" can mean out or off, but also "from" in a different context. "Er ist aus Österreich" means: "He's from Austria". It can mean out (like to put out a fire), or off (switch off a light)
