What's the "new ballot"? Here, we have a ballot on a single large sheet of cardstock. We take a Sharpie and fill in lines for the candidates that we want to vote for. When finished, we take it to a machine, stick it in the slot, and it sucks it in and presumably counts the votes. I like this method. As someone said, there's an audit trail and recounts are easy if necessary.
Never had touchscreen here. Before the current method, we'd go into a booth and flip levers, similar to marking the large card, then pull a lever to record the votes.
When I was in Mississippi, I seem to recall we used paper ballots and put them in a box with a slot on top, then later on somebody manually counted them. Nothing electronic about that at all. Of course, at that time computer punchcards were just coming into existence ....