AJAX :: Call Based On Results Of A Previous Call

The general framework is a simple user login function. The user name is selected and a password entered as usual. The function grabs the element values and passes them to a php page that queries the database. An AJAX call returns the password to the function and then I want the innerHTML to be a choice of two web pages, depending on success or failure of validation. There are existing AJAX functions available on the internet but they are overly complicated for what I think should be a simple, quick to load function.

Where I am stuck is that the standard procedure to make an AJAX call is the browser window event. How do you make the call from within the function? I have tried creating two new variables, "success" and "again" to replace xmlhttp, but still stumble on the event to assign a value. I left the blank password protection (if statement) with that variable to demonstrate what I mean.

I've put in my code below, which is in development and successfully alters the innerHTML text depending on user input but I can't figure out how to insert the relevant php page. I have '// out' the testing bits, but left them for info. (I have tried full 'scripting' as the innerHTML, but it's messy.)