"The rest is History." G-d caused them to speak different languages. Of course it is very difficult to complete a difficult engineering project if the workers do not speak the same language. If the foreman speaks yet another language it is still more difficult. So the project was abandoned and was a laughing stock to the ancients who abandoned the finest engineering project in history simply because of a "lack of communication." They all then packed out of town spread themselves around the countryside. The city was named Babel which in Hebrew means confusion.
What an ironic story! The building which they were using to avoid being spread across the world was the actual cause.
Why did G-d punish them for making a building? The answer, of course, lies within the text. They wanted to build a name for themselves. They wanted to be known as the worlds only and unquestionable Super-Power. Of course such an honor is reserved only for the One who said a statement and brought the world in to being. Many powerful and wealthy people love to have buildings and neighborhoods named after themselves. Indeed, this is popular today.
Professor Moshe Wienfeld in Olam Hatanach says that in the beginning of the stories of our Forefathers G-d says to Abram that he will agrandize Abram's name. This is diametrically opposed to our Pasuk where they want to make a name for themselves.
Hertz quotes Our Rabbis of Blessed Memory. They said that the building of the Tower and the attached self agrandizement was so central that when a man fell off the tower and died they would not get, even a little, upset. However, if a brick would get damaged they were very annoyed.
In our times we have seen people sell out their nations in order to win a Noble Peace Prize. We have also seen worse.