Well, take a meter to the dip switch itself - is it working (it's not unheard of for these to go back). Next, check if the change registers at whatever chip it's wired to (looking for bad traces).
There's going to be a resistor to +5 and another to GND somewhere along that circuit. Verify that they are both good.
With the system powered up, look at the pin that the dip switch feeds with a voltmeter. Check the voltage with the switch both open and closed. If it changes (which it should) from 0-5 (or 5-0), then the problem is likely the chip itself. If it doesn't change, then the problem is probably the resistors (to +5 or GND).