I've used a similar wireless system, and there's one workaround I know of that may work.
To do this, you change the MAC address on your computer to that of the DS or Wii (if it's running Windows, you can use a program called Macshift), whichever you're trying to connect, then login. As soon as you're logged in, disconnect the computer from the wireless and try to connect the DS/Wii (change the MAC of the computer back to normal if you want to use it on the wireless connection). With any luck, the network will remember that you were logged in by the MAC.
Now this is not a great solution, and of course you would need to repeat this every time you wanted to access the internet, but it could possibly hold you over until you get Opera (which I hope would allow you to login).