I'm not really sure why anyone ever thought that voting machines were a good idea. And by voting machines I mean anything from a touch screen to a mechanical hole-punching lever thingy.
Here in the UK, you turn up at your local polling station, and show them your voting slip, which you will have received in the post a few weeks earlier. You will probably have to join a short queue, the one appropriate to your street address. So you look for your street on a sign, and join the appropriate line. When you get to the front of the line, they look up your name in a big book. When they find your name they cross it out with a pen, and hand you your ballot paper(s). Very high tech.
The ballot paper is just a sheet of paper with a box next to each name. You put an 'X' in the box next to the person you're voting for, using a pencil which is attached to the desk in the voting booth with a piece of twine and some sticky tape. You fold it over once, exit the booth, and post the paper into a box. The box is sealed with a tamperproof fastener, and the only opening is a thin slot in the top.
At the end of the day, all the boxes get taken to the regional centre, opened, and the votes counted. By hand. If a recount is needed, that's done by hand as well. I can remember a few times when they've had about 4 recounts for a particular seat, because the margin was in the order of 10 votes.
I've been eligible to vote now for 14 years, and that's how it's *always* been done. You even recognise the same rickety wooden booths every time you return to the same polling station (in my case, the community centre round the corner from our house).
Even during a general election, the whole country's votes are counted by 2 or 3am. Now sure, the USA has a much larger electorate than us, but that also means they have a much larger pool to draw on for vote counting volunteers.