So yeah, this isn't fixed. In summary, I rebuilt Windows 7. Twice. And it still didn't solve it. I've just put on Windows 8, and it's still happening. Since this isn't all over the SWTOR forums, I starting to think that's it's a hardware issue with my PC, perhaps keyboard or something.
For reference, it did it with Windows 8 with nothing installed but the OS, drivers and the game itself. No other software.
For reference, it did it with Windows 8 with nothing installed but the OS, drivers and the game itself. No other software.