Did all bulbs burn out suddenly (over a short amount of time)? If so, there's something causing a surge in the power. If this is the case I recommend checking the size (amp) fuse to be sure it's not letting through a surge where it should be tripping the fuse.
If you want to check the switch before taking apart the dash, try finding the wires under the driver's side dash and trace them up to the switch as far as you can (so you get the right wires) and use an electric tester to see if power is going TO and FROM the switch. If you can't find the wires, try pulling apart the dash a bit at a time (starting from near the side door close to the slider switch for the running lights) until you can see the switch wires. You might be able to get to it without too much dismantling.
Let us know what you find.