The modem, cable, NIC, etc, won't do that, but their power supplies or the speakers might. You don't mention how far away "under the table" is for the speakers, but even shielded speakers can interfere. if this problem is always present then it seems simple enough to check- unplug ALL the external power supplies and move those speakers a lot further away. Also check that the monitor video cableisn't running parallel to AC power cords.
After ruling out these more obvious (potential) problems, you might quesiton whether there is some other strong magnetic field nearby, like a metal desk, something in a wall directly behind the monitor... if all else fails see if you can get your hands on a compass and see how it behaves in the vicinity of the monitor compared to other areas (with the monitor turned off/unplugged).
I suppose the more important question I haven't seen asked is, was the monitor always like this, or started after some change to the environment, addition to the system or moving of components?
If you rule everything else out, then it's time to check the monitor warranty for potential replacement.