Yep, I just played this game. I'm going to guess that you've run power into pin 1, and then used the ground wire on pin 4 to turn on your relay. Unfortunately, it won't work that way. Pin 4 MUST go to straight to ground if you want the illumination and/or the led to operate, as it's a common ground for both those items. If you have it wired as I suspect, you effectively have 12v coming OUT of pin 4 when the switch is turned on - therefore no difference in voltage, and no workies.
Pin 1 can be used to EARTH your driving light relay, then use the illumination wire in the dash to pin 2, and ground pin 4. So power is supplied to one side of the relay, then from the other side comes back to pin 1 on the switch. When the switch is pressed, pin 1 is connected to pin 4, and the circuit is then connected to ground. Pin 4 is always connected to ground, so the illumination will work any time there is power supplied to pin 2.
And if you want the led to work, you need to run a wire from the output of your driving light relay into pin 5, so any time the relay is switched on, it supplies 12v to pin 5, which is connected via the led to - yep, that's right, pin 4.
Clear as mud? I can do a sketch if it'll help. I actually ran two relays in the end - I wanted my driving lights only to come on with high beams, and by picking up the high beam wire under the dash, and sticking a relay in there too, I got away with only running a single wire to the front of the car where the other relay that actually turns the lights on lives. That wire is the earth side of the relays, so if it shorts all that happens is my driving lights turn on, no melties.
*EDIT* Interesting... I see someone has already put some pinouts up, but they certainly don't agree with how my switch was configured... Those pinouts I've given are taken straight from how it's currently wired in my car, but I think mine may be a rear wiper switch from memory, which may explain the difference? Best to check with a multimeter maybe...

