why exactly would you want to turn off your cable modem, if you have no internet activity going on, then nothing will go through. A NIC in a computer uses little to no resources. your modem is just a converter for the analog to digital signal for your computer, and it just runs cat45 to your computer. i really do not believe it will make a difference, press ctrl alt del (if you are in xp) and look at your performance tab, and then unplug your modem and see if their is a difference.
Mac G5 workstation with 4 gigs of ram, 4x250 gig drives in raid 5. High availability cluster server running centos for a server. 2xCanon GL2 cameras.