If my Home's Breaker Panel is not grounded, does my Meter Panel have to be? This may sound stupid, but I did not see any grounding on my Home's Breaker Panel or the Meter Panel outside on the pole. Is this possible, that neither is grounded? Wouldn't the whole wiring system not work properly in my house if there is no grounding? I guess my question is: Do I need to run a copper ground from my Home's Breaker Panel to a ground rod or run a copper ground from my Meter Panel to a ground rod? Or do I need to do this to both? Thanks,

Your house may be done with metal conduit as the ground, then you would have 2 hots and a neutral.
Do you have separate ground and neutral bars(Whites and greens)?

Yes!