How do I avoid Query scripts from conflicting with plugins in WP?

I have the following plugins installed and acitviated:

• Meenews newsletter subscription
• Lightbox 2 for images</li?

Meenews works fine with the following jQuery I have in my header:

<script type='text/javascript'>
		// Form 

		$(document).ready(function(){
        	$('#send_message').click(function(e){
				// Stop the form from being submitted
            	e.preventDefault();
	            var error = false;
    	        var name = $('#name').val();
        	    var email = $('#email').val();

            	if(name.length == 0){
                	var error = true;
                	$('#name_error').fadeIn(500);
            	}else{
                	$('#name_error').fadeOut(500);
            	}
            	if(email.length == 0 || email.indexOf('@') == '-1'){
                	var error = true;
                	$('#email_error').fadeIn(500);
            	}else{
                	$('#email_error').fadeOut(500);
            	}

            	if(error == false){
                // Disable the submit button to avoid spamming
                // Change the button text to Sending...
                $('#send_message').attr({'disabled' : 'true', 'value' : 'Sending...' });
                $.post("http://www.designcymru.com/contact/testr/send_email.php", $("#contact_form").serialize(),function(result){
		           	if(result == 'sent'){
                         $('#cf_submit_p').remove();
                         $('#mail_success').fadeIn(500);
                    }else{
                         $('#mail_fail').fadeIn(500);
                         $('#send_message').removeAttr('disabled').attr('value', 'Send The Message');
                    	}
                	});
            	}
        	});
    	});

 		</script>

…but when I activate Lightbox 2 it doesn’t work. If I add
var $j = jQuery.noConflict();
and replace all ‘$’ with ‘$j’ Lightbox works but Meenews doesn’t.

I am trying to figure out what I can do to avoid the jQuery<script> in my header from conflicting with any plugins. Any ideas? I’ve trailed the net and having no luck in figuring this out.