Sorry, I miss-read this post. I orginally thought it said your cable broke, meaning the coax that went to the back of the TV.
The coax input is more than likely a part of the main board. I am not a tv expert but as with laptops and input modules that break you have to soder the peice on or replace the whole board.
Easier to switch to a/v inputs as mentioned in Solution #1.
I could not find a spec sheet for your model but did find this for you to give you an idea on what is entailed in replacing a broken RF connection. This may or may not apply to your model, but here it is anyway.
http://www.youtube.com/watch?v=S9v-dUyzdrk
I would suggest letting someone who is qualified in TV repair fix it.
Here are the service manuals for your Zenith. Download both and then extract to your desktop for easy access. I downloaded and extracted myself to make sure it was a working copy so you are good to go.
Part 1:
http://www.eserviceinfo.com/download.php?fileid=34271
Part 2:
http://www.eserviceinfo.com/download.php?fileid=34270
Good Luck!
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