While waiting for a ticket response what you can do in the meantime to try to get the screen to load is the following. I know it's just the one character but hopefully something here works.
Delete the DiskCacheArena file under the swtor directory.
If that doesn't work, you can also try running a repair:
Non-Streaming launcher - Log into the launcher but don't click Play. Check for small letters "ST" in the bottom left corner. If this is NOT present, click the cog icon and then run the repair option.
Streaming launcher - If the letters "ST" is present, close the launcher, right mouse click on the game shortcut, select open file location and delete the BitRaider folder. Then start the launcher.
It's just that one character but it could be a glitch, another option to do as well is make sure swtor.exe and launcher.exe are part of the anti-virus / firewall safe list.
These are just basic things however but if its truly something with that one character and nothing above works, then unfortunately you may have to wait for a ticket to resolve the issue.
I know it's not what you want to hear, but fix by BW may be the only thing able to resolve it.
