Yes, the points that have been made by Maui are the ones I'd have made.

Assuming that the picture taken at ISO 400, with a shutter speed of 1/60th and an aperture of F11, is correctly exposed, I'd have expected the one taken at ISO 200 to keep the same aperture of F11, because you're in aperture priority mode, but change the shutter speed to 1/30th because you've halved the sensitivity and so need twice the exposure.

I'd not expect the exposure to change for the pictures you show, whether the flash was used or not.

Ah!!! Maybe a light bulb moment... perhaps, when you select the flash to be on, the camera is forcing the shutter speed to be 1/60th of a second. And, because you've chosen aperture priority mode, perhaps the camera is sticking with your chosen setting of F11, even if the exposure ends up being wrong. Think of it in terms of the old sci-fi computers that blow up if you ask them to solve a paradox that has no logical solution... the flash insists on 1/60th of a second... you've set F11 and it's not going to change that... result, incorrect exposure.

I've had a look at the manual, on-line, and can't see anything that gives enough information to either prove or disprove this theory. One experiment I'd try, if I were you, would be to set 'Slow Sync' and see whether this gives you better results. Hmmm... I've just read a review that says the D40 can use shutter speeds of up to 1/500th with the flash, so that would seem to disprove my theory.

Also, I think you should check that you have the flash set to be TTL rather than manual - this is Custom Menu, item #14.

The photos you've posted give all the info needed for someone in the know to solve the problem - as Maui has said, you now need to go to the Nikon board and find a guru. Good luck.