Probably a stupid question, but for the g13, do you also have any other gamepads plugged in (ie. ps3 controller)? FFXIV (and FFXI for that matter) tend to flip out and pick one as the only pad, so you have to make sure the 13 is the only one plugged in. (edit: this doesn't have problems with things like a naga mouse though)

If not, did you make sure to manually select FFXIV from the list on the g13 to activate it? I've had issues with the recent versions that even if you select it to auto load when a file is activated, it still doesn't and I have to manually select it from the list. (This goes for manually input games like ffxiv, and ones with preloads like WoW).