After all, roughly a third of Italians have never used the Internet at all – one of the lowest rates in Europe. Residents can recall providers laughing over the phone at their request for an Internet hookup, or the perplexed look of technicians upon arriving in Verrua Savoia, where just 1,500 residents live in dozens of small settlements spread over nearly 20 miles of valleys and steep hillsides in northern Italy.

Even so, some here believed they had the right to join the digital world, to pay their bills, do their banking or make a doctor’s appointment online.

One was Daniele Trinchero, a professor at the nearby Polytechnic University of Turin, who helped set up a nonprofit association that started last week and that offers fellow citizens what both the state and telecommunications companies have so far failed to deliver. The group may be the first of its kind in Italy.

Over eight years, he and his team have built a radio link with parts scavenged from computers and provided city hall with several routers to distribute the Internet to five access points. The access points, perched on peaks, direct the signal to homes with cheap receivers on their roofs or balconies.

“It’s simply necessary,” said the Rev. Corrado Cotti, 84, the parish priest, a former editor of the local paper and one of the pioneers of the experiment. “Print made communication easier,” he said. “But with the Internet, words fly.”

Well, sometimes.

Italy’s tardy embrace of the digital age looms as perhaps one of the nation’s most pressing, if unresolved, problems. In the 1990s, the leading telecom company was privatized, shifting the responsibility for connecting Italy from public to private hands. But Italy is a country where about half the land is mountainous, where the signal does not travel easily and where installing fiber optic cable is costly.

After years of unkept promises, the government of Italy’s youngest prime minister ever, Matteo Renzi, 39, is trying to put “digital first,” starting with a plan to invest more than 6 billion euros, or $7.25 billion, in ultrafast broadband connections.

But for now, the country lives with a yawning digital – and cultural – divide that has left behind not only large swaths of Italians, but also Italy itself from much of the rest of Europe and the United States. Italy has one of the lowest rates of ultrabroadband connection per household in Europe – half as many as, say, neighboring Switzerland. Only 10 percent of Italy’s primary schools have a broadband connection.

Introducing ultrafast broadband would “sensibly increase” the country’s gross domestic product, the government says, and it could also slow or reverse the migration to cities that has depopulated villages like this one.

“A speedy Internet connection makes all the difference in the world when you are in the final seconds of an eBay auction,” said Eldio Ginevro, 76, a former mayor and passionate collector of over 270 postcards of Verrua Savoia sent to him from all over the world.

“When Daniele first told me about his project, I thought it could revitalize Verrua and also make it more attractive for new comers,” he added. “So many have left this area recently.”

Verrua Savoia, like many other villages in rural areas, does not offer the comfort of city life. For people here, the introduction of a faster Internet connection was something of a utopian notion.

“When we moved here in 2003, there was no speedy Internet connection, and for our business it was a real problem,” said Marco Di Giovanni, who is responsible for international sales at a nearby packaging firm that paid to install a transmitting device with the Polytechnic University in late 2006, soon after the project began.

“How could we compete internationally if we couldn’t even hold a video conference?” he said. “That’s where you realize how crucial the digital divide is to your business.”

© 2014 The New York Times Company