I've seen before a topic here asking if there is any significant differences between using PALib or Nintendo's Nitro SDK... and that got me curious: what does it take to obtain the official SDK ?
Costs I can't speak on personally, and I don't know if anyone who is a licensed developer can either. But there are some requirements that I do know of. I don't imagine it is that expensive because from what I saw around the internet the development kit for the Wii is under 5k.
What will cost you however, is having a brick-and-motar location dedicated to your studio's work. Nintendo requires this of it's licensees.
Following that, they also request back financials so that they can ensure that you would actually have the resources to bring your game to market.
If you think you qualify, you can fill out the application to become a licensed Nintendo Developer.
$2,000 to $10,000 is the range given by Nintendo.
From Nintendo of America:
Development Kits: Approximate development costs range from $2,000 to $10,000, depending on the size of your team. Financial stability is expected by Authorized Developers in order to purchase the necessary development equipment for your project.
I'd say in most cases it's handled by the publisher. Don't have a publisher/want to self publish? Nintendo probably doesn't want to talk to you, then. If you had some industry connections it might be a different story, of course.
It's a case of "if you have to ask, you'll never know".
A couple of years ago I developed on the DS, the DS-Lite kit costed 1800$ which was way cheaper than any other dev-kit at the moment.
The Wii was a bit more expensive (I don't remember, 2500? 3500?) but you need to have at least two types, one for development (the black box) and one for creating the masters (green I think but I'm not sure).
For what it is worth: Unofficially "everyone knew" that you had to request twice for being granted to be an authorised Nintendo developer...