Try going to the battle log first… the battlelog is needed to do anything on bf4
Did you check if you have the battlelog plug in installed? There should be an orange flag button for an update
On the battlelog website check for an orange flag on the top of the page. If there is none you probably have it installed already and that’s not your problem
Don’t use the shortcut. Log into Battlelog and play either mp or campaign there.
All the shortcut does is open up Origin and a browser window with Battlelog.
Battlelog is a website used in bf4 to replace an in game menu (no idea who thought it was a good idea) after the browser plugin is installed you should be able to play.