The Rice University Neologisms Database

To destroy an object such that it cannot be repaired. To break something beyond all hope of repair. The extraneous verbal suffix ‘-ate’ added to the verb ‘bust’ suggests carrying out the action of ‘busting’ multiple times, which would naturally result in more damage to the object being ‘busticated.’ The headphones being referred to had been broken and repaired multiple times, until finally no amount of glue could hold them together. The speaker wanted to emphasize this fact, and needed a stronger variant of the word ‘busted’ to emphasize that the damage was irreversible.