Error messages (trying the Bank right now) -
003-4099 - A communication error has occured.
There may be problems with the network or the environment. To ensure an optimal connection environment, move closer to the access point and make sure there are no obstructions between the system and the access point. If this does not work, please try again later.
The other message I've gotten is 'no access point in range', and I've gotten both messages standing less than three feet from my router.
Attempting to download Smash Bros Demo -
Error 007-2916
An error has occurred. Please try again later. For help, visit support.nintendo.com.
YouTube worked fine.
EDIT: YouTube worked fine for a few minutes, then I got --
003-1099 No access point in range.
(Repeat first paragraph under first error message.)
The access point may be experiencing problems, such as the wireless signal dropping. Please refer to the instruction booklet that came with the access point.
The SSID may have been entered incorrectly. Check the settings in System Settings -> Internet Settings
(Note - I am using a wireless thingie to connect this computer to the same router that the 3DS is trying to access.)