Yes and no. There is definitely piracy at an individual level, but there is also piracy by organized criminals.

Copying a file from a friend is an example of the former. But that has been happening for quite some time. Copying an audio cassette or a video tape is an example that predates (most people's use of) computers. Photocopiers fall in that realm too.

Going to a website or a peer-to-peer network though is a different story. A lot of that is organized by people who have the intent to copy material on a massive scale and for profit. That sort of thing happened in the past too.

So nothing is really new here.

Well, one thing is new. Law enforcement has had trouble keeping up with the Internet. In the beginning, they didn't handle it properly. It was probably a matter of scale and technical competence in the beginning, which didn't help matters. But even once they got over those issues they were dealing with a bigger problem: crimes that could once be handled locally now had an international element. Sometimes they couldn't reach the people facilitating these activities, or it was a tediously long process if they did. Couple that with proactive civil rights movements which suddenly considered copyright infringement a speech issue, and enforcement because a big issue.

I would argue that this lead to another consequence: there was a cultural shift because the anonymity of the internet and the lack of effective enforcement gave people the perception that copyright infringement was okay. And that, I would suggest, is the real cat that got out of the bag. Computers and the internet have very little to do with copyright infringement other than being a tool -- one tool among many.