I had this issue too. Here's what Customer Support told me to do:
Please delete the following files from "%userprofile%/AppData/local/SWTOR/swtor" if they exist.
If this does not get you back into the game, please login to your launcher and run the repair function through the menu accessible via the cog button on the bottom left of the launcher.
It fixed it for me.
EDIT: I was also told to delete DiskCacheArea from C:\Program Files (x86)\Electronic Arts\Bioware\Star Wars - The Old Republic\swtor