First thing, try a different browser, just to check that the script is working fine. I've had super good luck with both FireFox and Opera (Opera being the best for me).
I assume you've configured a department, and assigned an operator (the one your using) to it.
Do you have a URL showing your Live help icon?
Make sure your server is a "trusted site" from the menu bar, click tools, security, trusted sites, and add your domain (I add both domain and www.domain
and set the trust level high. If it still doesn't work, we should probably check on your styles.