I don't know if it counts as a parody, but SNL also did a great Star Trek
skit during its first season (Belushi as Kirk; Chase as Spock; Ackroyd as
Bones and the Voice of Scotty).
The crux of the story is that the Enterprise is being pursued doggedly
through space by a '68 Impala, which turns out to be manned by two NBC
execs who have arrived to cancel the show.
Subsequently, the set is dismantled and the crew are dispersed, leaving an
unbelieving Shatner (Kirk/Belushi) toenter his Captain's Log and ponder the
stupidity of such a move.
The other one that comes to mind, obviously, is the recent Simpsons episode
that features a TV ad for a geriatric future sequel ST film called (I
think) "Star Trek XII: So Very, Very Tired."
Good luck with the quest!
[log in to unmask]
New College, '90