So after doing a bit of research it appears that grounding is likely not the problem. I'll assume the cable is already run? Is the cable exposed, run underground, etc? The routers themselves are easily movable, could you bring the barn router to the house and verify that everything works when in close proximity? My first instinct on most networking issues is a cable problem. I assume this is a cable you terminated yourself and not a factory made cable. I'm kind of thinking aloud here, if the barn and house have different grounds then I assume there is no power run from the house to barn, correct? The reason I ask is to find out whether the ethernet cable is running alongside the power, that could cause interference and in many locales would be a violation of code. If all else fails I'd remove the connectors from the cable and crimp on new ones (assuming that you crimped them on in the first place) just to try and eliminate that as a source of the problem.