Does not autofocus

If it focuses OK in manual mode then there is a possibility that you have a damaged ribbon cable in the lens.

Does it shoot in manual focus? In which autofocus mode(s) does it not shoot? Are you trying to focus too close, or on a subject with insufficient contrast?

The D90 has three different autofocus modes. In the AF-S mode it will not shoot until it has focused. In the AF-C mode it will shoot when you press the shutter release button even if has not focused. In the AF-A mode the camera switches between the AF-S and AF-C modes so either can apply.Also, bear in mind that the camera doesn't really know what you're taking a picture of. It may focus on something other than your subject. If you're in the single-area AF mode then you control which of the eleven focus points the camera uses. In any of the dynamic-area AF modes the camera decides.For full details on how the various modes work, please consult your manual. You might also check out the Nikon D90 video tutorial.

Go to your settings when your in shooting-mode (Press the 'i' button on the bottom left).
There, change your focus mode from MF to AF-S or AF-C or AF-A.
Should work.

You can change this in the menu while in shooting mode. This is from page 48 of the manual:

Choose how the camera focuses.

A (auto) M d (Shooting menu) M I Autofocus mode

A Single AF (default setting)

The camera focuses when the shutter-release button is pressed halfway.

B Full-time AF

The camera focuses continuously until the shutter-release button is pressed down

halfway. Use with moving subjects. The sound of lens drive movement will be heard

while the camera focuses.

That's just the quirky autofocus of the d80. Try tilting the camera diagonally to focus and tilting back up to shoot.
Unfortunately, autofocus issues like those are the difference between a d80 and a d200/d300 :/

Panfocus mode on the F505 appears to convert the lens to a fixed-focus design, (everything in reason is always in focus) presumably by stopping down, and perhaps by doing other lens adjustments. So "panfocus" must mean "the whole world is always in focus", instead of "quickly focus as you pan", as at least one reviewer has misinterpreted it. This feature is very handy for a couple of reasons. First it eliminates the autofocus delay, cutting the shooting time down to just the shutter release delay. And second, it allows for shooting in total darkness, since the image is always in focus.

1. Typical problem subjects for autofocus 1) Very low-contrast subjects 2) Overlapping nearby and distant objects 3) Very bright subjects in the center 4) Subjects moving very fast 5) Subjects through glass Focus on an object that is at the same distance as the desired subject, apply Focus Lock, and then recompose the picture. Or set the lens focus mode switch to (or), and focus manually. (Manual focus is only possible with cameras providing this feature.) 2. Attempting to take pictures out of the camera's shooting distance: When taking pictures out of the camera's shooting distance, the subject will be out of focus. The shooting distance differs from each camera model. Please check the specifications of your camera in the instruction manual to determine the shooting distance.

1. Typical problem subjects for autofocus 1) Very low-contrast subjects 2) Overlapping nearby and distant objects 3) Very bright subjects in the center 4) Subjects moving very fast 5) Subjects through glass Focus on an object that is at the same distance as the desired subject, apply Focus Lock, and then recompose the picture. Or set the lens focus mode switch to (or), and focus manually. (Manual focus is only possible with cameras providing this feature.) 2. Attempting to take pictures out of the camera's shooting distance: When taking pictures out of the camera's shooting distance, the subject will be out of focus. The shooting distance differs from each camera model. Please check the specifications of your camera in the instruction manual to determine the shooting distance.