If you go into the Bios as the laptop boots (hit F2 at the startup Dell screen), and scroll down to the Wireless menu, you can modify two important settings. Make sure the wi-fi and bluetooth (if you want) are both Enabled. Then a few entries down there is a "Wireless Switch" category. Change this setting to "None." Then, go to the "Wi-Fi Catcher" category, and change that to "Off."
This will cause the laptop to completely ignore the hardware switch on the side, and force the card to stay on at all times. Voila! Now it doesn't matter if your switch is broken.
Meanwhile, if you never NEED to turn off your wireless card, you can just right click on it and disable it from within your network adapter settings. So, no harm no foul.