ways to finish a complete major league baseball game with no pitches.

I think by one pitcher, or even both it could actually be 0.

Isn't there some kind of rule that a ball will be charged if the pitcher does not deliver a pitch in a certain time period. Taking that rule in effect the pitcher does not have to throw a pitch to walk a batter. He then picks off the runner. He does this over and over again until everybody walks and gets picked off. So he could go through a whole game without ever throwing a pitch.

The opposing pitcher could do the same thing but make an error in a pick off attempt moving the runner to second, the catcher can then make a wild throw on a steal attempt to third with the runner scoring.