Well, the audio is most likely tied to some other issue that involves electrical, and without more information, I'm not going to speculate. I will say using a headphone OUT from the laptop is BAD unless you're using an active direct box on each channel.
If you're not too concerned about syncing lights to audio(and don't), then you can get away just fine with MyDMX running in the background, it will work just fine if you're using a zippy laptop and a firewire drive for your media.
The audio hum issue is NOT tied to the lighting software. Those are two sepparate issues, and since it's possible you're on different breakers and maybe even different panels, that could be a major cause of the problem. An Ebtech Hum eliminator can be a good tool to addresss this issue if we're at LINE LEVEL.