What is my logon domain?

This is the farthest I have gotten In connecting to the internet

Here's some background:

Hi there! In my sister's room is the router for our house. My mom's laptop can connect to our wifi as can the three iPhones, the Wii, and the Nintendo DS's. Buuuuuut my computer wont. I have a Belkin USB adapter. It can find out network and the neighbors, but it wont connect to ours. Jut to give it a shot, I tried to connect to a neighbor's. I got to the enter password screen which is farther than I can get on my own network.

My sister used to have the adapter and i had the router could that be the problem or atleast part of it?

Any help would be greatly appreciated. Thanks! Jenna

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It fails "due to an unknown reason"

every time.

Where do I find the model number?

What am I supposed to do with the MAC address?

Do you think its the router or adapter?

...

Now it is asking for my User Name, Password, and Logon Domain.

I thought the username and password were the name of the wireless connection and security code. Help me out please!