A couple weeks back the office I work in lost the network connection. Technically we had a network, but DNS was slow to resolve, and we definitely couldn't get to the Internet.
I had a bit of an epiphany about how I work during this outage. I could still work slowly, but I certainly wasn't effective. I decided that I subconsciously solve problems.
My habits are to work for a while, but when I hit a stumbling block in what I was trying to accomplish, I would change contexts entirely and hit a blog, Twitter, or some other site for a couple minutes.
During this break from my work, my subconscious would solve the problem, or at least get me refocussed and when I resumed my task I would pick up and continue right where I left off.
Not having the Internet actually slowed my work down considerably (and not because I couldn't Google the answer).
Several productivity sites I frequent all suggest that the Internet is a distraction and it must be blocked to allow yourself to realize your full productivity. I don't fit that mould.