They are not going to say there is anything wrong with the DSi settings. When they say "The error code range 52XXX normally refers to a problem with the IP settings on your router." We translate that to mean, "The settings in the router and the settings in the DSi are incompatible."
When they say "We recommend that you manually enter your IP Address, Subnet Mask, Default Gateway and your Primary and Secondary DNS servers in to your console," we translate that to, "The DSi can not reach the DHCP server.
Whent they say, "There is a problem with the wireless channel or mode being used, we think, "Someone is using a device that operates on the 2.4Ghz range - the same range as the router. You can "Try changing the channel on your router to either Channel 1 or 11," but often you will still have connection issues. Disreguard the part that says, "these would not be affected by any similar devices in your area using the same channels," it simply is not always true. Wireless N operates on the 5Ghz range. Unstable? I don't know. B and G in Mixed Mode is best for now. Use Key 1 in your WEP key list (log into the router and verify that you have the correct key - #1 on the list!
In the Setup tab, under Wireless Setup, change the SSID to something you recognize so you can be sure you are not connecting to a neighbor's router with the same defauls SSID.
Set the chanel to 1.
Set the 802.11 Mode to "Mixed 802.11G and 802.11b.
Set the transmission rate to Automatic.
Verify the 1st Key generated againsk the one you have been trying in your DSi.
Click on Apply Settings.
When it verifies that the settings were suseccful, clasoe the window and unplug your router. Wait at least 20 seconds and plug it back in.
Once the router is back up, Verify that your PC can connect to the internet.
Setup the DSi. At the Setup screen, tap Nintendo Wi-Fi Connection Settings, tap one of the Connection slots, tap Search For An Access Point, and select the SSID you just created.
You should be connected. If the test fails, let us know what code you see.