How to hook up a cable splitter?

I am trying to hook up both a TV and the Internet in my home office, but I only have one cable hook-up. I bought a splitter so I could do this, but the signal is apparently too weak to support both the computer and the TV, because the TV picture is fuzzy.

My first question is: Is it possible to do this without altering anything?
My second question is: Is there some secret way of hooking it up to prevent the signal from being weakened? Or will I have to buy a signal amplifier?
My third question is: The splitter is, I guess, designed to do something with a satellite and an antenna? Did I buy the wrong thing? :(
 
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