I'm starting to think that Tenacious D isn't a parody band after all. Please don't misconstrue my meaning here; I've always taken the band seriously. Part of Tenacious D's charm is how consistently incredible their discography is despite the overtly humorous subject matter and silly execution the band trades in.
The reason I'm starting to question the D's status as a parody band isn't related to the quality of their music but rather the length of their career. There are tons of "real bands" that don't last nearly as long, boasting albums that inspire people to laugh at them and not with them. And on the other side of the fence, Jack Black and Kyle Gass are still pumping out classics that are just as fun as their earlier work. In the video linked above, you can check out the music video for their song Video Games, which perfectly coincides with Black's role as Bowser in the Super Mario Bros. Movie.