Hello and welcome to JustAnswer!
When you replaced the lock cylinder what did you get? Did you have a dealer or locksmith build you a new cylinder using your VIN number? Or have you purchased something that came with keys?
Was your original ignition key that you always used gray and thick-headed?
Ok. Your Durango has the Sentry Key Immobilizer System (SKIM). There is a transponder chip in the key that communicates with a module in the steering column which then communicates with the engine controller to allow the engine to start and run. When an unprogrammed or incorrect key is used the engine will start and die.
If the replacement keys you got with this lock cylinder are thick gray-headed ones then they will need to be programmed to the vehicle using a dealer scan tool. If the keys with this new lock cylinder are plain keys (without the thick gray head), they are incorrect for your vehicle and won't work. You have to have a good programmed SKIM key to allow the engine to start and run.