The touchscreen is needed as much as Internet connectivity, which is to say not at all. They just add more points of attack.
A tabulating ballot box with auditable open-source software that scans a printed ballot (probably scantron, but the tech has flexibility now) and prints out a receipt for the voter to check immediately for errors before allowing the ballot’s final deposit will do the job just as well. At the close of polls the ballot box spits out its (non-binding until otherwise agreed upon) results which are phoned into the central tabulating office and confirmed by multiple confirming election officials at the local station. It isn’t 100% secure but nothing is, and it’s more secure than anything involving Windows XP and Access 2000 and a Comcast Internet connection.