If mouse over for over 2 seconds then show else don’t?

You need to set a timer on mouseover and clear it either when the slide is activated or on mouseout, whichever occurs first:

var timeoutId;
$("#NewsStrip").hover(function() {
    if (!timeoutId) {
        timeoutId = window.setTimeout(function() {
            timeoutId = null; // EDIT: added this line
            $("#SeeAllEvents").slideDown('slow');
       }, 2000);
    }
},
function () {
    if (timeoutId) {
        window.clearTimeout(timeoutId);
        timeoutId = null;
    }
    else {
       $("#SeeAllEvents").slideUp('slow');
    }
});

See it in action.