I have the exact same issue; use Origin in online mode and my avatar is gone, career stats are missing, the three DLC packs I bought are missing along with the free Koenigsegg.
Switch to Origin's offline mode and everything works as EA/DICE intended.
EA state the game servers for PC are up and operational so I'm at a loss to explain what is going on.
Upon going through an extensive process with a very helpful EA advisor, I've nutted out that the data within my save game has corrupted somehow. A few times my internet would die just as the save game was uploading..I wonder if this was the cause. If Orign remains offline, no issues with my save; go online and all the DLC cars disappear along with my play time stats.
If I start a new game which creates a new save file, all the DLC cars and my stats appear, irrespective of whether Origin is online or offline.
So I have two choices; remain online with Origin and start a new save or keep Origin in it's offline mode and finish the remaining events.
Hope this helps others who may encounter a similar situation.
