Benjamin,
The wall warts are not all well filtered, so that probably accounts for the hum.? It seems like you audio may not be the problem, because the receiver is naturally quiet if the grounding is good.? You should check the connection of the antenna to the board, because maybe you have a bad solder joint or broken wire. The brwon lead should go to the center of the antenna connector.? Also, there have been reports of poor quality BNC connectors, so you may want to test that or just replace it with a better one.
Dan, W2DLC