It took me a while to finally figure out how to set up the Wi-Fi connectivity on DSi with my LinkSys WRT54G access point.
If you use WPA encryption on your WRT54G, you need to set up the Connection 4-6 instead of Connection 1-3.
Go to the System Settings, navigate to Internet.
Click on Connection Settings; click on Advanced Setup; click on Connection 4 and choose Search For an Access Point; select the SSID from the search list;
Enter the pass phrase when prompted and save the settings.
When prompted to Connection Test, click on No.
Click on User Agreement and choose Language and I ACCEPT. This is a critical step, which took me all the time to figure out how to connect to the internet!