WNR2000v4 Computer constantly connected to modem.

You can always unplug the Ethernet cable from your computer.  :-)

If you want to shut it off in Windows, start by right-clicking on the pitch fork icon and click on Open the Network and Sharing Center.  You will see something like this: 

Click on Change adapter settings on the left.  You will see something like this:

Click on the icon that looks like the one labeled Ethernet in this picture.  Your icon may have a different name.  If you have more than one icon that looks the same, click on the one without the red X.  Once you click on the icon, the option Disable this network device should appear.  Click on that.  Verify that Internet access has been disabled.

You can enable Ethernet by repeating this process.  You will click on the same icon (except that it will show a red X) and then click on the option Enable this network device.