Does the iPod show that it's connected in the top left corner (there should be three bars that look sort of like a fan next to the word "iPod" there - it's tough to describe but you'll know it when you see it)?
If not: Go to "Settings", then "Wi-Fi", and it will begin to search for all the networks around you. Sometimes mine needs this little kick start to pick up networks, especially if I've just taken it out of hold or turned it on.
If yes: This is a bit more complicated and instead of typing it all out now, I'll wait until I find out what's up.
Let me know if this works, if not we can keep working away at it. Unless your mom got a lemon with a busted wireless card right out of the box (which is really unlikely), it will work, just a matter of trying a few things.