I don't think it's a good idea to break off the ground of a 3-prong plug. Although it's unlikely that you'll have to use the safety benefits of the ground, if you do have to use it, the ground could save your life. Personally, I'd look to see where the cable enters the house. Ground the cable at that point to the house ground. You could also add another ground rod (hammered into the earth), but the ground rod and house ground should be connected using thick-gauge wire (#6 I believe) according to the National Electrical Code (NEC). Plus, if you don't ground to the same point, you increase susceptibility to ground loops.
At my house, grounding the cable to the earth ground (itself grounded to the house ground) solved any hum caused by the cable box.