Split AC current from one wire into two wires (+ and - DC wires) using bridge rectifier
New and novice,

Until you get yourself a nice clean EARTH ground, you will be beating your head against the wall.

You MUST either get to a cold water pipe, as close as possible to your project, then after removing oxidation from that pipe at the connection point, connect the ground connection(also made free of oxidation), and use a nice big gauge wire, to insure the cleanest ground source possible. How electrically clean your ground is hinges on having the lowest resistance to earth ground as possible. 
The alternative is to use a additional grounding rod. Those are generally specified to be 5/8" diameter, driven in a minimum of 8 feet. And the code generally specifies two of them. That gives you an idea of how critical they are. So adding one more to the spot of your project is probably your best bet. 
Although I find it hard to believe your cable company is the source of your noise issue, it is likely a contributing factor, and houshold nuetrals are notoriously noisy. 

DO NOT even think of cutting the current ground point to your house as you had mentioned! If the house ground is compromised at all, or what you do causes the current connection to corrode over time, the neutral line in the house will start having a voltage on it, and could become a shock hazard.
Especially during an electrical storm, or power line surge. Your TV's computers Etc are also likely to start going toe up. Line surges are the #1 cause of appliance failure.

Without a clean ground to start with, capacitors would be of no use.
If you have no clean ground, you are tying noise to noise through a capacitor. Ferrite beads are only of use for small ammounts of high frequency noise.           

I think you get the idea.  Also more info on what you are trying to accomplish would be helpful. : )
-Sara H