Could you add an option so that if its a brand new ticket, it would show one certain triangle "!" icon in the pop-up alert... Whereas, if its a reply to an existing ticket, it'd show a different icon -- such as the same current icon but a red instead of yellow background for new tickets, and the current yellow background for replied/updated tickets...
I leave up my pop-up boxes (infinite display time option enabled) and it'd be an easy way to see how many red's I have, and how many yellow's I have at a glance, and also it'd help me determine which to work on first.
(I am awaiting approval of my bugs.kayako.net account so I can also submit this as a feature request)