Oh no, planes would still fly.
There would be no programmed overbooking, so you would always be on the plane for which you have a ticket.
No wrong bar codes on the baggage tags, so the baggage will arrive with you at your destination.
There would be a third man on the flight deck navigating the airliner with a compas and star tracking.
Long distance communication would be on the telex machine, and only essential information would be received. We would hardly receive any junkmail.
Airbus planes would be grounded for a short while as they would need to have Boeing flight control systems installed.
Some things would take a little more time, but just imagine all the time we would save when we didn't have to deal with computer problems...
Always keep your number of landings equal to your number of take-offs