My friend recently deleted my account off of their 3ds and added their own, but I still can't link my current account with my new 3ds. I am currently afraid to do an account transfer because I don't want to take her account and put it on mine.
You can call Nintendo at their service line (1-800-255-3700) and they can help "unlock" your account from your old DS. You will need your Nintendo Network ID, birthday, possible your email, and you will need to tell them a couple of your past transactions.
This is all to verify that it is your account and not anyone else's. Also, they might ask for your new system's serial number, so keep it next to you while on the phone- this is how they tie your account to a specific system.
All you need to do is tell them that you do not have your previous system so it is impossible to do a system transfer. It's been a while (over a year) since I had to do this, but it is not really difficult, just more of an inconvenience. Please let me know if I can help more.