What specifically do you mean that when you use your battery powered amp, the hum does not exist? For instance, can you use the battery powered amp to listen to TV without having the hum? Does your TV control the sound? In other words, are the outputs of the TV connected to your amp?
Basically, what to do is to ensure that the cable coming into the home is grounded to the electrical/house ground. Typically, the electrical/house ground is a copper rod pounded into the ground near the fuse box. However, one can also ground to a metallic pipe, given certain conditions. Regardless, you want to ground the cable to this electrical/house ground.
If this does not fix the hum, strip the system down to something that works without the hum. Then add items into the system until the hum comes back. Whatever you just added is what causes the hum.
Also, the cause of the hum may not be what you think it is. I had hum in two subwoofers caused by bad interconnects. In my situation, I started with a complete system, and kept taking stuff out of the system until the hum went away. I was shocked when I realized that the interconnects were causing the hum. Nonetheless, replacing the interconnects stopped the hum.