Bad picture with Sega Genesis model 1

I bought a second hand Sega Genesis that came without an RF cable (for picture and sound). I remembered when I previously owned a genesis, the Sega RF cable worked for my NES but the NES cable did not work for the Sega, but I figured I'd try anyway. The picture came up exactly how I remembered when I tried doing that when I was younger, jumbled up. I've bought two different RF cables to try and fix this problem, both claiming to work specifically with a Sega. One was from radio shack, another generic one I bought off ebay. Both gave the same jumbled picture as if I was using the NES RF cable.
Could the problem be the console's hardware? If so, what could I do to fix it myself?