Actually ASP.NET will post-back if you use its built-in JavaScript __doPostBack function. There's no other painless way for doing that.
That means you can use jQuery to handle drop-down lists, buttons or whatever (X)HTML element event and handler's body will invoke __doPostBack.
It's unclear that you want is a full-postback, but a partial one using AJAX.
If you're looking for a solution for sending form values to the server without a full-postback, I believe you've these options:
Anyway, let me give you an advise: ASP.NET works quite different compared to PHP and you'd not try to reproduce some known PHP solutions in ASP.NET. You need to change your mind.
About showing a DIV or anything while something is processed, play with initializeRequest ASP.NET AJAX PageRequestManager:
But that would depend on what AJAX API you're using, because since Microsoft AJAX will be replaced by jQuery in the next times, I'll need to say that you need to do that in some jQuery approach, like creating some $.ajax wrapper so your code will be able to listen when an asynchronous request is going to be made and you can perform actions by handling that situation like showing a DIV or any loading notice.