I have a 2WIRE what's next?
There are three possible reasons why your DS cannot find your access point.
1. Your router is not compatible with Nintendo products.
2. Your router has "disable broadcast" selected.
3. There is interference from other wireless devices or objects (such as microwaves).
So. Step 1: Is your router on that list? Click on 2Wire and make sure that your router's serial number is actually on the list.
Step 2: If your router is on the list, make sure that "broadcast" is selected in the settings instead of "disable broadcast". I don't know how to tell you how to do this because I don't know what type of router you have yet. If you tell me what kind of router you have, I might be able to figure out how to do this.
Step 3: If your router is near anything that could interfere with it (such as a microwave), move it somewhere else in the house away from other wireless devices.
The last option I have is to see if your router is WEP or WPA encrypted. The reason that this is my last-ditch effort is because the DS Lite should be able to pick up WPA-encrypted access points and tell you that it sees them, it just can't connect to them. Your DS is apparently not picking up your access point at all, which is why you need to try to enable broadcast. If you have a DS Lite, you can ONLY pick up WEP encryption. Here's how to go about changing your router from WPA to WEP.
Go back to that Nintendo Router website that I sent you to and click on "2Wire". This should bring you to a list of 2Wire routers. Your router should have a sticker on it somewhere that says what type it is. Find that router on the list and click on it. (If your router isn't on the list, then chances are, it's not compatible with Nintendo products). It will bring up a new page, and on that page there is a line that says "Access login by clicking" and there is a series of numbers starting with 192.168 after it. This is your router's IP address. Type in that series of numbers in a new tab in your browser. This should bring up your router's settings. It may ask you to log in. Your username stays blank, and your password is "Wireless". If you live with someone else, they may have edited this and actually given the router a username and password. If you can't log in, ask your parents/roommate/spouse/whoever if they gave it a username and password.
If you live with your parents and they also use this router, changing any settings now could kick everyone off of the Internet, so please get permission before doing this.
Also, *disclaimer*:
I do not take responsibility for kicking you offline if you reset something on your router that you weren't supposed to. I do not know what kind of custom setup your router may have and if changing settings might mess it up. If you choose to change your router's settings and something bad happens, it's not my fault. Okay, now that said:
Go back to the Nintendo page about your router. Click on the word "example" next to "WEP/WPA key". This will bring up a screenshot of what I'm about to tell you to do in case you get confused. Now go back to your router's settings, click on "Home Network"at the top of the page, and then click on "Wireless Settings". Now look at the "Wireless Security" section of this page. Next to "Authentication", does it say "WEP", or some version of "WPA"? If it says "WPA", then that is why you cannot connect with your DS. If it already says "WEP", then maybe we'll have to troubleshoot something else. If it says "WPA", change it to "WEP". If there is more than one WEP option, choose "WEP-Shared".
It will now ask you for an encryption key. Select "default encryption key", and look on the bottom of your router. There should be a sticker there. Underneath the barcode, there is a group of 10 numbers in brackets. It should look like this: [2222222222], except with different numbers and not just twos. Type this into the "Key" box. DO NOT CHANGE ANYTHING ELSE. Now click "Save".
Your router should now be WEP-encrypted. You should restart it at this point to make sure that it actually puts your changes into effect. If it is kicked offline, then you did something wrong. It shouldn't be offline just from changing the encryption, though. Now go to your DS and delete any settings you may have already had for an Internet connection. Create a new connection and it should find the access point.
If that doesn't work, let me know and I'll see what else I can come up with.
EDIT: If you do find an access point, your DS should call it "2WireXXX", where the three Xs are some numbers. It should have a red lock next to it - the red lock means that it's WEP security. Choose this and type in the WEP key (the numbers in the brackets on the bottom of your router) and you should be connected.
I think I missed something here, why do you need wi-fi to MM? You can still breed for shiny pokemon without a foreign parent, and with the shiny charm, you still get a pretty nice little boost.
My guess is that he/she wants a foreign Ditto to breed with, and he/she can only get that on the GTS, which you need Internet access to use.