The actual access to the internet is controlled by hardware not a browser.
Your Tiger Mac should be able to connect to the Internet via ethernet or compatible wi-fi through your router.
Even your old web browser should still be able to access certain very old and not updated websites.
Once connected, using a web browser is only one way of accessing content for the internet.
Yes, to access web sites you need a browser that can open them, and most browsers that work on a Mac running Tiger, would no longer be able to open regular websites that are using current technologies to produce the website and its content, the browser has no knowledge of.
Unlike a TV, the Power Mac cannot simply receive a video input and display its content. The boxes used with TVs are in and of themselves computers that send a video signal to the TV. The Mac is also itself a computer, and what you are asking amounts to connecting a new computer to your old computer.
Any reasons you need to use your Power Mac to access the internet?
Also, what exactly do you want to accomplish by doing this?
There may be an easier way to do what you want.
For now, you can use http://frogfind.com to browse the internet using your very old web browser on your Tiger Mac, it will attempt to translate most websites to something that web browser can interpret and show.
Don't expect full functionality of all the websites however.