Do I have to add a ground wire that has been missing for 20 years?
You need to run a ground wire. NEC 250.114(C) requires dishwashers to be grounded.
You cannot use a GFCI protected circuit as a replacement for a ground. When the GFCI method is used in place of a ground for a receptacle the NEC makes a very specific requirement to label the receptacle &quot;No Equipment Ground&quot;, then follows with an informational note to refer to 250.114 that gives a list of equipment that requires an Equipment Ground, which includes dish-washing machines. Usually the installation instructions included with the dishwasher will also instruct to connect an Equipment Ground, the code requires following the installation instructions since they are part of the Listing (UL or other).
You can connect the Equipment Ground to another ground originating at the same panel, to the ground bar in the panel, or to the grounding electrode conductor.