Here is what I am trying to do in ASP.NET:
Create one page called Main.aspx. This page has a DIV and a buttons.
The browser loads Main.aspx. Then when I clic
As far as I know, barring the use of iframes, there is no way to load one aspx page into another.
With postbacks or ajax, you can use UserControls (ascx) instead. They can contain pretty much the same content a page can anyway, or use a MasterPage.
If you wish to have no postbacks, ajax is probably the way to go, though again, it does not allow you to load an aspx page into another, only to change the content of the page you're on (amongst other things).
I'm not sure about other platforms for web development though, they may have a solution closer to what you want to do, so if asp.net is not a "must", you should consider checking out other platforms.