Why is the load circuit on my GFCI outlet dead?
My standard advice on hooking up GFCIs (of any type) is leave the warning tape on the LOAD terminals and hook up the GFCI LINE only.   Then, run the GFCI through its paces.  Make sure it tests and resets definitively.  If it has sockets, make sure you can plug in a (non-ground-faulting) load in and have it work.  

Your testing of which was LINE side was correct, since you confirmed one side was LINE.  I would hook up only that cable, and nothing else for now.  Then see where you are. 

If you do not get a working GFCI able to power things, then attaching anything to LOAD would be counterproductive.  Don't even think about it, it's not worth the brainwave. 

Just make sure you are clear on which side is which.  People do get them confused.