You'd be wasting time pulling new cables that's ridiculous. Nothing wrong with your coax cables, but they may need re-terminating (new connectors) ans possibly adding or removing signal distribution devices such as splitters or amps. Below is part of my recommendations from an old post I've had.......
3. If you want to send the cable or sattelite feed with a high quality signal to other televisions, I suggest doing what I've done and add a ZeeVee HD RF modulator. This will insert your own HD channel (I use channel 10) on the RF system that feeds all televisions. This way you only need one sat or cable receiver (which is all you can have if you use a dish tailgater system, which I also recommend).
4. With only one sat or cable receiver you'll eventually want to add an RF universal remote control, such as those from Universal Remote Control compan (URC).
Your manufacturer probably did, more than likely, wire it correctly, but they often use cheap crimp connectors instead is compression fittings. Wherever you have poor signal you just need to cut off and replace the connector on the back of the wall plates or at the splitter.
I'm not a site vendor. My company does sale these products, but I recommend finding someone locally that could help you with all this. I have owned a commercial A/V integration and engineering business for more than 10 years.
Hope this helps.
