I see, then at this point I do not know what to tell you
@mungry. The NNID service and how it handles linking and sign in/out, particularly the lack of an ability to actually sign out, is a royal pain in the ass. My only suggestion is to try calling nintendo and tell them your younger sibling/cousin managed to format your system and you are now unable to sign back into your NNID.
From what I understand this is occasionally a valid consequence of formatting a system and Nintendo is fully capable of (and often more than willing to) remotely unlink a NNID. They will need your NNID account name, email address, birthday, and some purchase/payment info to verify. Any demos or games you have downloaded at any time will show up in their records and can be named if they ask you to list some purchased content to verify the account.
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I just noticed in your signature that you have two 3DS systems, are you trying to sign into the N3DS with the same NNID you are using on your O3DS? Because you can only link a NNID to a single 3DS system.