Aperture priority mode keeps producing underexposed photos?

Aperture priority mode keeps producing underexposed photos?
Added (1). it's a nikon d40 and for some reason when I try to switch to Auto ISO it tells me it can't be used with the current settings, though I know it can. Trying to shoot outside in natural overcast sunlight so I set the ISO to 400 but no matter whether I try a small or large aperture the photos keep coming out nearly pitch black.
Added (2). in manual mode, i can achieve a proper exposure with a large aperture but when i try to use a small aperture, it still comes out dark though that may be due to my lack of expertise. It's for a class assignment where we are supposed to use both a small and large aperture to compare depth of field using aperture priority mode, and i really can't figure out why it isn't working

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