I have applied my nation to the UN about 10 different times and I always get a welcome message but no e-mail to complete the application!
Please send all advice to Republa.
First, check your nation settings and make sure that you have entered an e-mail address, and that the address is correct. If it is, your e-mail is probably being blocked by an anti-spam filter. This might be something in your e-mail client, but more likely is a program running on your ISP's server. Anti-spam filters aren't perfect, and so sometimes block e-mail from NationStates. Unfortunately there's not much you or I can do about this.
I found this in the FAQ under technical so might give it a shot & if not i am not sure what it could be.
if all else fails, create a free account on www.hotmail.com or something. they have pretty leniant spam filters.