Unfortunately, but there isn't a way for you to recover your Nintendo Network ID, as it is locked to the original Wii U console that it was created on.
No guarantees, but perhaps if you give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, or use their webform to find out if they can transfer your NNID to another Wii U console, and if they can, what type of proof you might need to give them.