Reactivate Satellite Dish

The satellite dish only receives the signal, it is the receivers that decrypt the signal and have an access card that is activated with your programming package. 
But, to answer your question, as long as the dish is a modern SWM HD slimline directv dish, it can likely be reused. The tech may need to reaim it when reinstalling service to ensure optimal reception. 
In the case that the dish does not have a clear view of the southern sky or is too high up for the technician to access, another dish may be used..

The dish itself is just a receiving mirror, nothing to activate itself. Depends on if current SWM, good condistion, and aim if it can be reused.

As you canceled well over 24 months ago, your account cannot reactivated. You would be starting over at this point. Contact DirecTV to discuss your options.