I've never even thought of that. How exactly do you do that Salty? I have cable and internet together, and I have a modem on my tower connected to the internet. I also have another computer connected through it so how could I say turn mine off while keeping the other one on? Hopefully that makes sense.
How is the computer you play on connected to the modem? With a cable? Wireless? With a cable, I'd just try unplugging the cord (after letting others know just in case it crashes the network, but it shouldn't or your computer could never shut down without killing everyone else's internet). I've never really played around with turning off internet off of a wired connection (the name for being connected through a cable).
Wireless, you should be able to disconnect from the network. Usually that's down at the bottom and at least on Windows 7 it's a signal strength bar.
I personally never played without the internet. My old desktop probably would have played the games easier with it off, but the wireless adaptor I had was a pain in the rear to get to connect to the network. I had to jump through hoops to get connected to a wireless network.
My new desktop doesn't have an issue playing the game with internet running.
But if you are having lag issues, turning off things like the internet isn't a bad idea. Just remember to occasionally keep it on when you load the launcher if you get your patches through the launcher.
