Is your firewall blocking access to the game? (EoCApp.exe and SupportTool.exe both need access)
If the game can not connect to Larian's chat server, it disables global chat (which happened a couple nights ago to me when my internet went down for an hour or two).
Try starting the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file by right clicking and running it as administrator. Maybe that will make a difference, if the source of the problem is in your system.