I don't know what the limits are for a background image, but trying to load one that size into almost anything makes little sense to me. If I was trying to do it, I'd make a copy of the image, reduce the size to 2,000 pixels or less and then load it as a background image.
Yes, definitely try shrinking the size per Mark's suggestion. Even if you cut it down to half that size it should load. FM uses Window's own image loading routines, which tends to have limits to the size of image they can load.
An alternative is to slice that big image up into tiles, and place the tiles as individual map objects, rather than assigning the big single image as a background image. Put them on their own layer and mark the layer as unselectable.
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An alternative is to slice that big image up into tiles, and place the tiles as individual map objects, rather than assigning the big single image as a background image. Put them on their own layer and mark the layer as unselectable.