coachred,
I'm not sure whether you are a zero turn newbie or not, but if you aren't sitting on the seat (which you most likely are), and don't have the control arms in the most outward parked position when you disengage the parking brake, the engine will cut out. Its supposed to work this way.
If you are doing as I described above, logic would say that either one of the control arm switches (one each side) or the switch on the parking brake is defective or grounded. I would pull your side covers to those and check to see if you have a broken/missing wire, corroded/broken switch (Check for continuity as you cycle the switches. They should have an open or closed condition, that changes as you cycle each switch. If you find one that doesn't change, its the culprit.)
Beyond that, you'll need someone with more electrical knowledge and specifics than I possess. Good Luck!