Your first issue—clicking the shutter button doesn't actually trigger a shot—could possibly be a hardware problem. Usually, the camera will not shoot until it has acquired autofocus. If something is interrupting this process (such as a faulty lens or problems with the body's AF sensors), the camera will hesitate. These are best diagnosed and fixed by a camera technician.
The second problem is that you have likely set a very long shutter speed (display shows something like 10″) or a very small aperture (display shows f/32 or other "large" numbers).
As others have noted, it simply sounds like you're not familiar with the camera. Reading the *whole* manual, front to back, is the best thing you can do at this point. The first problem you asked about could also be caused by trying to focus on a flat, plain surface with no detail to focus on, or trying to focus on something too close to the camera (inside of a meter).
Even the best cameras have limits on their performance. It is best to practice shooting outdoors on a bright day. Humans and cameras have very different ideas of what "good light" is—a CFL desk lamp may provide adequate light for us, but the camera will definitely not have enough light to make a good exposure. If the camera has trouble working when trying to shoot a sunlit subject, you know for sure that the camera needs service.
Personally, I would suggest setting the camera to Program (P) mode and seeing what settings the camera chooses in different situations. You can switch to Manual (M) mode to have complete control over exposure settings. Get acquainted with how ISO affects exposure and noise. Also get acquainted with the Exposure Compensation (+/–) function, which is helpful when shooting in P, A, or S modes.
Should you get in trouble with exposure settings (e.g. you're getting completely black or white photos), hold down the QUAL and Exposure Compensation buttons to quickly reset settings—your images won't be deleted. These two buttons are marked with green dots for quick reference.