If I began an action, failed it, and was unable to ever do it again, my action would be completed (but it would be completed in a way that I wouldn't expect). Would I use the perfective aspect for this?
Well, if there's a result then it's perfective. But note two points:
- Quite often you have to use several verbs to describe all your started/completed/failed actions. Then it's quite possible you have to mix perfective and imperfective forms together. E.g.:
Я там был, мёд-пиво пил, по усам текло, в рот не попало --> I was (impf.) there, I had (impf.) mead and beer, it ran (impf.) through my mustache, but it didn't get (perf.) into my mouth
- Sometimes you have no real result, but rather a sentence "results" in some state and/or repeatable action. Then it's imperfective, of course. E.g.:
Порой не верится, друзья, но всё-таки бывает --> Sometimes it's hard to believe (impf.), my friends, but it happens (impf.) anyway