Problems with my nikon d300?

A nikon d300 and I'm learning to use it but this has been happening for a while like it will work one day and the next it won't. Like I'll click the shutter button and it will auto focus but won't actually take the picture. I know its not that I'm not pushing the button it must be a setting that I'm not familiar with and accidentally set. Does anyone know how to fix this, what its called, or where in the manual I can read about it? Also another side problem is that sometimes the actual shutter takes a LONG time for a camera (sometimes about 10 seconds) and the picture always comes out blurry because I can't keep it perfectly still for that long. So I'm wondering how to fix it so the shutter only takes a fraction of a second. Thank you So much in advance. Also its not something with the mechanisms of the camera, it has something to do with a setting because this happened to my Nikon N6006 (the film one) like how it wouldn't take the picture when i clicked the button. I must have switched a setting by accident.

I think you need to have a good read of the instructions.
The d300 is a very upmarket camera, you are lucky to have one.
Sounds like you have it on manual mode with shutter set to 10 seconds or something.

Set to auto mode, and the focus to single shot af then see what happens.

Try using flash, or upping your ISO, anywhere between 100 and 400 for daylight.

Long shutter speeds are caused by low light, have you been shooting indoors?

The camera also may not fire if it can't focus.

Did you read your user manual to see what conditions the camera will not let you take a shot?

No memory card is one, fully discharged battery is another. The lens not being in focus and another, the exposure being out of range when you are using the camera in the shutter speed priority mode is another.

If you are using the aperture priority mode and have the lens stopped down to where the proper exposure time is ten seconds, that will cause long exposures. That substantiates the blur. Camera movement during the long exposure.

You really need to take a basic class in photography. All the problems you list are the result of not knowing the fundamentals of photography

If you shoot in the manual mode and use the cameras light meter much of this will be corrected. If you shoot at shutter speeds over 1/250th second, you will see very little blur in your photos.

Here is how to balance the ISO, shutter speed and lens aperture so you do not have these issues any more.

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

Basically you have been trying to fly a 747 with only a motor vehicle licence.