HappyAlbatross is right: you definitely have a grounding problem, either due to missing proper ground or having a ground loop somewhere. Also if you're using a switching power supply and/or a class D amplifier (that is, a switching amplifier [1]), they can be real nightmares if not properly filtered, and cheaper ones almost never are.
Grounding and ground loops, filtering and decoupling are complex issues which would need entire articles, but there's a lot of stuff on the net to get you started.
Long story short: don't throw away your board, the problem could disappear just by changing a power supply or rewiring ground connections.
[1] They use the same identical principle behind switching power supplies but applied to driving speakers: performance is fantastic compared to current draw, but they tend to produce lots of harmonics and RF noise just like switching power supplies.