I tried to check my yahoo email this morning and my Safari asks me to either upgrade or continue without upgrading. I am using a Mac PowerBook G4 running 10.4.11 I clicked on continue without upgrading and the screen does not change. I restarted and then clicked on Upgrade and the same result....screen never moves to another?
Safari 4.1.3 is the last version of Safari for Mac OS X Tiger, so you're out of luck on that end. Furthermore, Chrome and Firefox (in their current versions) do not support Tiger either.
You can try looking for Mac OS X Leopard, since Safari 5.1.10 (the last version of Safari for Leopard) is available for download, but that's as far as your computer will possibly be able to go, since the latest version requires, at minimum, OS X Mountain Lion, which requires an Intel processor.
If you don't like any of these options, you'll have to purchase a new Mac.