I haven't read through the entire code, I haven't seen the HTML, so I'm gonna go on under the assumption that you have those under control. The problem is quite simple as far as I can see.

function abc(){ }; defines a function.
abc(); executes the function.

What you're essentially saying in your code is:
But you never call the function.

Just remove "function validate_form ()" and the corresponding braces and the browser will execute your validation code.