protect IP address with Knoppix 7,3 ?

Can I protect my IP address from being obtained while on
the internet using Knoppix 7.3 Live DVD ?
Or will I have to buy a router ?

I don't think that you have a good grasp of what an IP address is. With or without a router, your IP address is sent to any site that you visit. This is a basic internet concept, it is important to do this so that the site can respond to you.

With a router you assign yourself a block of private IP addresses, and those IP addresses can not be routed over the internet. But the router still uses your public IP address to reach other sites.

To hide your IP address you need to use a tool like TOR (a.k.a. The Onion Router) or a VPN. But if you use a VPN you still communicate via your public IP to the VPN and the VPN then relays everything for you. TOR can make it much harder to track your IP address, but you have to trust that the TOR nodes that you use are trustworthy and not compromised, and that is difficult to do. The major league snoops like the NSA know about TOR and they are actively working to not just compromise it but also to track everyone using it. So think about what you are trying to do and why you think it is important to hide your IP address before you blindly trust TOR or a VPN to hide behind.

Looks like the internet is nothing more than a big spy tool. Why can all those
badnick hackers get away with everything and I can't even visit Martha's
Naughty Picture site without being tracked by everyone ? It's not fair. And
I'm must be missing some pieces of the puzzle. How can those banking sites
say they are "Secure" ? All I want is some privacy once in a while. Otherwise,
I don't care about being tracked. You can watch me watching the BBC site
all day if you can stand the bordom.
In conclusion, you say there is no proven way to protect my IP address.
So be it. Thanks for taking the time to tell me the unpleasent truth.
I appreciate it.