Turntable Hum

I've got an old Technics that is giving me fits...there's a slight hum present, that's there regardless of whethter the unit has a headshell attached or not, and regardless of whether it's AC power is plugged in. When I swing the arm across the platter, the hum varies from crackling and loud to nothing. It's not near a transformer or anything like that. Any ideas? I'm really perplexed by the behavior of the arm.
Has it ever behaved and if so, what change happened that initiated the problem?
No, I don't have two grounds run. I'll certainly try it, but I guess I ruled it out since the hum doesn't change when I unplug the unit.

We have a less-than-a-year old baby, so I'm not sure when the problem cropped up, since I don't get as much time as I used to. I'd love to be able to trace it to one event, but I can't.