dishwasher hardwiring help
Dexter- I honestly don't know why such a cable was run to the dishwasher location. A 3-wire cable, with a black, red, white plus ground is nomally two hots (black and red) the white neutral, and the ground. In your case, the black apparently is not hot. You can try connecting the red of that cable to the black of the dishwasher to see if the red wire is the hot wire in your case.
Is there a switch above the countertop for a disconnect for the dishwasher? Some electricians are fond of locating a dishwasher disconnect switch along the countertop.
Do you have any testers? Multimeter, neon light, etc? Might check to see if either the black or the red are hot before you go to the trouble. For all we know, the other end isn't hooked up in the panel. If there was never a dishwasher installed there, the cable may well not be terminated at the other end yet. That would be standard procedure for new construction or a major remodel, for safety's sake.