<apex:page controller="Captcha" cache="false">
<apex:pageBlock title="Captcha Verification">
<apex:form >
<apex:pageBlockSection columns="1">
<apex:pageBlockSectionItem >
<apex:outputLabel for="inputStore" value="Store Number"/>
<apex:inputText value="{!myStore}" id="inputStore"/>
</apex:pageBlockSectionItem>
<apex:pageBlockSectionItem >
<apex:outputLabel for="inputpassword" value="Password"/>
<apex:inputText value="{!myPassword}" id="inputpassword"/>
</apex:pageBlockSectionItem>

<apex:pageBlockSectionItem rendered="{! NOT(verified)}">

<script type='text/javascript' src='https://www.google.com/recaptcha/api/verify={!publicKey}'>
</script>
<noscript>
<iframe src='https://www.google.com/recaptcha/api/verify={!publicKey}' height='300' width='500' frameborder='0'>
</iframe><br/>
<textarea name='recaptcha_challenge_field' rows='3' cols='40'></textarea>
<input type='hidden' name='recaptcha_response_field' value='manual_challenge'/>
</noscript>

</apex:pageBlockSectionItem>
<apex:pageBlockSectionItem >
<apex:commandButton action="{!verify}" value="Check If I am not a robot" rendered="{! NOT(verified)}"/>
</apex:pageBlockSectionItem>

<apex:pageBlockSectionItem rendered="{!verified}">
<p>
Have Salesforce Address information display here 
</p>
</apex:pageBlockSectionItem>
</apex:pageBlockSection>
</apex:form>
</apex:pageBlock>
</apex:page>

public class  Captcha
 {
    public boolean checkCurrentValue{get;set;}
    public String challenge{get;set;}
    public String response{get;set;}
    public String publicKey {get;set;}
    private static String privateKey = '6Ld0wgkTAAAAALlZg3d1iZBxEfTkK2Qy_vZ4SCFP';
    private static String baseUrl = 'https://www.google.com/recaptcha/api/verify';
    public String myName { get; set; }
    public String myEmail { get; set; }
    public String myStore { get; set; }
    public String mypassword { get; set; }
    public Boolean verified { get; private set; }
    public Captcha()
    {
        publicKey = '6Ld0wgkTAAAAAGkcvz8yxeZUSVpWQmCdxOkw9MIH';

        this.verified = false;
        checkCurrentValue=false;
        challenge = ApexPages.currentPage().getParameters().get('recaptcha_challenge_field');
        response =  ApexPages.currentPage().getParameters().get('recaptcha_response_field');
    }
    public PageReference verify()
    {
        System.debug('reCAPTCHA verification attempt');
        // On first page load, form is empty, so no request to make yet
        if ( challenge == null || response == null )
        {
            System.debug('reCAPTCHA verification attempt with empty form');
            return null;
        }
        HttpResponse r = makeRequest(baseUrl,'privatekey=' + privateKey + '&remoteip='  + remoteHost + '&challenge=' + challenge + '&response='  + response);
        if ( r!= null )
        {
            this.verified = (r.getBody().startsWithIgnoreCase('true'));
        }
        if(this.verified)
        {
           How do I return the Salesforce Account address fields based on the Store Number and password that was entered by the user on the VF page.
            
           // Account act= getAddress();
            
            return null;
        }
        else
        {
            // stay on page to re-try reCAPTCHA
            return null;
        }
    }
    public PageReference reset()
    {
        return null;
    }  
    /* Helper methods */
    private static HttpResponse makeRequest(string url, string body) 
    {
        HttpResponse response = null;
        HttpRequest req = new HttpRequest();  
        req.setEndpoint(url);
        req.setMethod('POST');
        req.setBody (body);
        try
        {
            Http http = new Http();
            response = http.send(req);
            System.debug('reCAPTCHA response: ' + response);
            System.debug('reCAPTCHA body: ' + response.getBody());
        }
        catch(System.Exception e)
        {
            System.debug('ERROR: ' + e);
        }
        return response;
    }
    private String remoteHost
    {
        get {
            String ret = '127.0.0.1';
            // also could use x-original-remote-host
            Map<String, String> hdrs = ApexPages.currentPage().getHeaders();
            if (hdrs.get('x-original-remote-addr')!= null)
                ret =  hdrs.get('x-original-remote-addr');
            else if (hdrs.get('X-Salesforce-SIP')!= null)
                ret =  hdrs.get('X-Salesforce-SIP');
            return ret;
        }
    } 
}