I had the exact same problem.. I called Tech support and all you have to so is:
-Right Click on the desktop Icon > Select Open Location
-Find the Folder labeled "BitRaider"
-Delete it completely.
-Re Launch SWTOR. It will start a Verifing process, let it go through completely. Takes about 5 mins. It will then start a download starting in the 90% complete range. Let it compete fully. When the Play button is clickable, then go into the game. Once your Character screen comes up, the notification box for the 99.99% complete SHOULD be gone. And your game will be fully patched.
Again... this fix is right from SWTOR Tech Support.