Switching out the disposal isn't that hard if you have a half-decent toolbox, but it's kinda hard to
explain. You can pick one up at Home Depot or Lowes for abt $60 for a 1/3 HP model that does
pretty good. Read the instructions, and it's pretty self explanatory.
Once that is replaced, before you lock it all in place, there is an inlet port on the side where the
discharge water hose from the dishwasher is connected to. There is a plastic plug in that, for those
who don't have dishwashers. Pop that piece out, then plug the wastewater hose from the dishwasher
hose to there.
It'd be my guess that since the disposal isn't working, there is some obstruction to the wastewater
from the dishwasher, so it's not draining properly. That's why it smells like crap.
Just a guess from a semi-edumucated home-tinkerer.....