Problems w/ shutter speed & aperture on my camera

I'm currently enrolled in Art Institute of Pittsburgh for photography and on shooting assignments we have to shoot in Manual mode. (I have a Nikon D300)
My problem is with the aperture and shutter speed. Now, I know how to change both of these settings, but my aperture will only go so far.
Example: When I change my shutter speed to 1/13 the aperture won't go any lower than 3.5 which makes a dark image.
1/60 shutter speed, aperture won't go lower than F4.

Does anybody know what I'm doing wrong?
Please, this would help a lot on my assignments.

What is your assignment exactly? I don't know the specs of your specific camera but with a 1/13 shutter speed and at f-3.5 your image should be very bright, unless you are shooting in very low light. Check to see if your Neutral Density filter is on. It's usually a little numbered scroll reel marked "and" on the side of the camera, make sure that is at 0.

I think you need to spend some time in these two websites to understand how to use your fine D300 and its controls

http://camerasim.com/slr-camera-explained.html

And how to balance the ISO, shutter speed and lenses aperture

http://camerasim.com/camera-simulator.html

Your aperture is limited by the range on the lens. My Nikkor 300 mm f/2.8 has apertures from f/2.8 to f/22. Any requirement of a smaller or larger aperture to take a proper exposure will have to be substituted be either changing the shutter speed or ISO setting

Apparently your instructor either hasn't explained the Exposure Triangle or you didn't pay attention and take notes. These sites will help you understand the relationship of ISO, Aperture and Shutter Speed - the 3 "legs" of the Exposure Triangle:

http://www.digital-photography-school.com/learning-exposure-in-digital-photography

http://www.thephotoargus.com/101/understanding-the-exposure-triangle/

http://www.kamerasimulator.se/eng/?page_id=2 This interactive site will also help you to understand depth of field as well.

Maybe you need good stabilizer… Hmm see on this site