Javascript as Jquery Function Call?

See the Codex section on jQuery noConflict wrappers in WordPress:

[…]if you really like the short $ instead of jQuery, you can use the following wrapper around your code:

jQuery(document).ready(function($) {
    // Inside of this function, $() will work as an alias for jQuery()
    // and other libraries also using $ will not be accessible under this shortcut
});

So, in your case, you could use

var seq = 0;

jQuery(document).ready(function($) {

    $("html").niceScroll({styler:"fb",cursorcolor:"#000"});

    $("#mainlogo img").eq(1).hide();
    function goSeq() {
      var nxt = (seq+1)%2;
      $("#mainlogo img").eq(seq).fadeIn(2000);
      $("#mainlogo img").eq(nxt).fadeOut(2000);
      seq = nxt;
      setTimeout(goSeq,2500);
    };
    goSeq();

    $(window).load(function(){
      setTimeout(function(){
        $("#gmbox div").animate({'top':60},1500,"easeOutElastic");
      },1500);
    });

    function trackLink(link, category, action) {
      try {
        _gaq.push(['_trackEvent', 'tracklink' ,'click',link.href ]);
        setTimeout('document.location = "' + link.href + '"', 100)
      }catch(err){}
    }

    $('[rel="outbound"]').click(function(e){      
      try {
        _gaq.push(['_trackEvent','outbound','click',this.href]);
      }catch(err){}
    });

});

…assuming that all the rest of your JS code is correct, of course.