I see losing the internet to be a very serious problem, mostly for the businesses that rely on the internet. Amazon.com, for example, is just an online store (it has no physical store you can walk into). If the internet failed, then boom. There goes their business. And it's not just Amazon that will suffer. Many online stores will also suffer.
And what about antivirus and anti-spyware programs? Viruses and spyware get on the computer via internet. If the internet goes, well while it stops viruses and spyware from getting to the computer, the usefulness of antivirus programs and anti-spyware programs will have passed, thus businesses like Norton, AVG, Panda, and MacAfee will lose a lot of money.
And then there are the companies that make online games. If the internet blows, then they start to lose money because people cannot play the games anymore.
There's probably more that I have missed.