I recently got a new lens for my Nikon D3300. I now have 3 lenses; the other two that I have came with the camera and work great but when I put my new lens on, it will only manually focus. If I go to the menu to change the focus mode, it won't even let me change it to auto focus. The lens is a "Nikon AF Nikkor 70-300mm 1:4-5.6 G" lens - as it says "AF" on the lens I believe it should auto focus. What could be the cause of the problem here?
Unfortunately, that lens will not autofocus on your camera. Nikon make two basic series of autofocus lenses: those with "AF" in the name, and those with "AF-S" in the name. The "AF-S" lenses have the autofocus motor built into the lens, so can autofocus on any camera. The "AF" lenses (as yours is) require the autofocus motor to be built into the body, and the D3xxx and D5xxx series cameras do not have the autofocus motor in the body.