You don't need your Security Key to reset your password, you just need access to the email address that is associated with your SWTOR account.
Just go to https://account.swtor.com/user/password/recover and enter your Display Name (not your email address). The Display Name is identical to your forum name, and then check your emails.
By the way, your SWTOR account is attached to your EA account so you can also just try to login e.g. at Origin with your email address and restore the password there. But for some older accounts (which you seem to have) this may not work.
And yes, if everything else fails, calling Customer Service is the last resort. They can restore the account for you, you just have to be patient and the waiting time is not too bad. For telephone numbers, see the bottom of http://www.swtor.com/support
