Have you already tried the tips in this guide.
@YaiZ1 I'm not seeing any login attempts to the SWTOR account linked to your EA profile. What's the Display Name you're trying to log in with?
I'm no longer receiving my one time password, my computer was away getting fixed and I need to install the game again. My username is sleekricco and I am a long time Premium member.
Have you followed the steps per this guide here?