help me oh internets...

So, my router died. My computer is too old for the OS to be (or be made) compatible with a new router (at least none I can find). I can't afford a new computer just now. Fine, I can live with computer tied to ethernet wall cable for a while. But, the Tivo needs its internet, too! My Netflix streaming needs it! So, I got an ethernet splitter, which is much cheaper than a new computer. But it doesn't work. Or, only one of the two  jacks in the splitter works, so it's not actually splitting anything.

Before I take it back and get a new one, in case the splitter's defective, does anyone know what I might be doing wrong, or if what I'm trying to do just won't work?

Anyone?