To do something like this you will need to create a php API to handle login and database storage. I beleive i have this at my work if you would like a copy premade with an example on using it.
If you would like to make it yourself you are going to need to use the _POST["Value"] to get input from the ajax plugin in construct 2 that will in return send anything you print our in php back to construct 2
well assuming that you can construct the PHP (a there are some available scripts to do it), you can construct a request to the C2 game. The browser object will let you access the request string or perhaps more usefully just the parameters you are passing in the string