The parts list say it's supposed to be a 1K... anything could have been installed, thoguh. What does it read as far as numbers? 103?

Can you use your voltmeter and measure across the leads of the LED? (This may not do anything... I can't remember). The voltmeter injects a small voltage to calculate the resistance. This should be enough to get a reading.

Please test on the LED side of the resistor pack with each leg to each terminal on the pack. You have to make sure there's continuity there (0 ohms). Maybe you did that and I'm not understanding you properly. If you have 5V going into the pack but do not have SOME voltage on the positive leg of the LED (which is also the terminals on the distributed side of the resistor pack) then there is a problem with the resistor pack. If you have voltage on the negative lead on the LED then there is a ground issue. Have you measured continuity from the negative leg to ground?