This certainly sounds like a ground loop issue, did atmasphere's suggestion work?
I moved to a new place a few months ago - and purchased a new TT to celebrate. I had an incredible amount of issues with what I had anticipated would be a trouble free TT, and assumed I should just have gone ahead and gotten the finicky belt drive rig.
My issues were very much like yours, it all started with a cartridge issue which I somehow made worse. For some reason, it decided it no longer liked the way it was grounded. And the interconnects that were fine yesterday are also an issue. I had one advantage in being able to quickly swap out cartridges which aided in my troubleshooting. I swear half the time it seems like voodoo.
I'll run through a few things to try - also don't discount the cartridge giving you problems. Is this both channels? Can you get it to change? A lot of times, you're going to get a slight hum/buzz at volume with an analog rig, but it shouldn't be noticeable at low volume.
Separate ground cable, interconnects and power as much as possible
Change out interconnects (they are shielded, correct?) and reverse
Change ground wire location if possible
Check cart wiring, reverse cart wiring (just to see if anything changes)
Relocate TT if possible - even 2' can make a difference
Unplug all of your digital gear and anything not needed
A lot of troubleshooting doesn't necessarily fix, but gives you clues that something else might be the issue. Also, does anything change? Meaning, is it quieter sometimes, noisier others? Do you have any sort of line conditioning?
In the end, my problem was 1) 2 new cartridges that failed in almost identical fashion, 2) needing a very well shielded interconnect cable (this was sporadic) and 3) relocating my ground location to phono stage power supply from preamp. Hopefully you've already solved it and it was your ground wire.