This might help you - I found that some code generation requires ALL departments to be online or the button will show offline. Others, by the way, do not. As I recall, the text generation is accurate.
Rather than spend a bunch of time on this now, I decided to create only 1 department. It works for me -- for now --- for that site.
Also, I want the nice little window to pop up for the chat, so I messed around with ripping code from one generation and sticking it in the other. I finally have a simple combination which seems to work for me for the moment.
Your problem seems to be that you have dept's 1, 2 and 3 and your operator is assigned to 1 and 3 or just 1 but not all 3. As such, some of the indicators generated by HCL will show OFFLINE. And, from that, I had my simple solution - get rid of dept's 2 and 3. Actually, for another setup, I simply have all operators in all departments. Workable, not exactly what I'd like (I don't want the user seeing "departments" which are for my use -- really different websites. I can't get away from that if he will, at some point, be asked to chose a "department" to chat in or email to. )
-- Joe B.