Camera Problem Nikon D90?

I have a used Nikon D90 with a 10 or so year old 52mm Sigma auto focus lens. I just acquired the camera and I'm trying to take pictures with it but whenever the center of the image becomes far away, the camera will not take the image. I can hear the motor in the lens trying to turn the focusing dial but its not moving. I just don't get it because I see the image in the viewfinder and I'm saying "take" but it just makes a little noise and doesn't do anything. I've tried it on the P, S, A, and M settings, which I don't think should matter.

Thank you

Added (1). I have been looking at the manual, in case you were wondering.

If it focuses on close items, it may not be getting enough contrast from the far subject to focus. Try the different focus modes to see if you can get better results. Ultimately, you can manual focus. You know you can download a manual from Nikon, right?

If it's having problems focusing at far distances, perhaps the lens infinity stop is set too close which will prevent the lens from focusing past a certain distance. In order for your camera to take a picture, the camera must have focus lock (little green dot in the lower left of your viewfinder). There's a way to override focus lock in your menus, but, then you'll get fuzzy images. See if you can find something online to explain how to adjust the infinity stop on the lens.

You can also set the camera to manual focus to override the focus lock check.

PASM settings won't make any difference.