cannot install

For download application, we must:
1. Download Now Click Download Now to begin downloading application
2. When finished, there will be the .dmg file to your desktop (or Downloads folder). Then double click the application for Mac file to begin installation.

At first, I always do that ways to get many applications. There is no problem. I just download, then install it. Very simple.
But, I think now there is problem with my mac. After doing the first step, I cannot do the step 2. When I double click on the application, there is no installation begin (nothing happens). Why does this happen?

 

I think application that have been dowloaded must be installed, such as yahoo messenger and videora. But, they can not installed. If I double click on them, nothing happens. that is so weird.

 

thanxs very much. I know that, but I think you don't know what I mean.
At beginning. I always do what you say. But, after I got messenger virus (I opened link that my friends sent), my mac is going error. Software runs slowly. Software also always suddenly closed and then there is crash reporter boxs, such us for mozzila firefox. Now, if I finished download software, there is nothing happened if I doubled click on it. Before, if I double clicked on it, there will be a box like you have sent. Of course, I can run that software easily. But NOW, cannot. (Now, I have changed my messenger password)
My mac also always must be restarted. Sometimes if I switch on my mac, there will be some weird sound. I knows that something wrong happens. Anybody can help?