When you hit up a site, such as cnn.com, does the TCP/IP packet contain the MAC address of your network card?
Could cnn.com theoretically record my MAC address?
In IPv4: Nope. They will see the MAC of the device which forwarded the packet to the server, likely their border router.
In IPv6, the 64 bit "host" part of the full 128 bit address is often automatically generated from the MAC address, and hence might be visible to the server one connects to. See also How to avoid exposing my MAC address when using IPv6?
And how do you know that CNN is not executing ipconfig /all from the browser java scripts, and collecting the data, then parsing it and recording the MAC?
You can start by purchasing the computer with cash anonymously somewhere. Go to a public Wifi and use that for access.
And finally, somehow lock down your ipconfig commands. This may not do the trick though because a smart enough programs can go straight into a particular memory address and read it. I suspect the MAC address is always placed in the same address of memory and can be retrieved. You need to set up your OS so it will not allow direct access to memory without the highest level of access, then never go to a website while logged in to admin level.