Andy,
I've no experience with the 2407wfp, but it should give you a reasonable display through the composite. Is there a button that needs pressing to select that particular input to be displayed?
Have you tried connecting to the composite on a TV? If you get no output, then I'd suspect there's a fault with the Amiga.
One of my A600's has just lost its green signal, causing the composite output to have a light purple hue. Not sure whether it's the RGB output at fault or the circuitry that creates the composite. I guess I'll find out when I finally get around to hooking it up to my LCD TV via the scart.