I doubt the only prompt you're getting is "Invalid", so what is the full message?
Try switching it to WEP if at all possible and try to connect then. DS models before the 3DS had problems with WPA.
Your router has no WEP option at all?
Try Shared. If my suspicion is right, that's WEP (generally routers have options for WEP-Open and WEP-Shared). If not, it's worth a try anyway.
Any error messages?
When I type in the pass on the computer, it says "Error, the network key you entered is invalid. Type the key again, using 5 - 13 characters"