Wall-mounted? Mic positioning is extremely important. You could be picking up all the things bunt posted about above, you could be picking up a neighbors ceiling or box fan, and since they're mounted to the wall they can pick up any amount of vibration in and outside your home. You could also have a grounding issue in the electrical system in your home or inside the device itself and those can be expensive to have fixed. I would go with some of the above advice and pick up some mics that you can move around preferably with shockmounts (you don't have to have them, but they help a great deal) and a preamp thats not attached directly to the innards of your recording device.
Try to borrow a preamp from someone and see if the buzz is still there. Switch cables just to try it out, may be a grounding issue in the cable. Unmount the mics from the walls and place them on the floor or on a stand of some kind to see if that helps. The EQ suggestion is a last resort if you absolutely can't fix the problem with any of the aforementioned solutions.
Usually try the cheaper suggestions first. Chances are it really is a simple problem with a simple solution.
Good luck with the buzz, I know how annoying it can be.
