There is a musical piece that I has brought me to the brink of
insanity in my quest to find it and its name.  It was played recently
in an episode of NBC's The Restaurant and also in an old Looney Tunes
episode wher Bugs Bunny is rubbing something onto some guy's head. I
believe it begins with high c, high c, high c sharp, high c, and then
repeats that.

Hi torturum:

[And my wife always made fun of me learning my classical music from
Bugs Bunny cartoons!]

The cartoon you have in mind is "The Rabbit of Seville", during which
is played the Overture from Gioachino's Rossini's opera, "The Barber
of Seville."

The note sequence actually has another "high C": 

"high C" "high C" "high C" "high C sharp" "high C"

A "poor" quality version of this piece can be found at:

Gioacchino Rossini 
URL: http://www.karadar.com/Dictionary/rossini.html

Of course, better performances can be purchased at any classical music
store. :-)

See also:

The Barber of Seville by Gioachino Rossini 
URL: http://www.npr.org/programs/attheopera/archives/010526.ato.html
Quote: "There's no counting the number of ways this song's been
lampooned. Probably the most famous concerns an "uppity wabbit" trying
to elude a hunter with a speech impediment by masquerading as a
barber, of course. That's right: Bugs Bunny and Elmer Fudd in animator
Chuck Jones' classic parody, "The Rabbit of Seville" -- it's a truly
hilarious sendup."

I hope this puts your mind at rest. 

[Shhhhhhhhhhhhhh......I'm hunting wabbits......]

websearcher-ga

Search Strategy (on Google):

barber of seville bugs
"barber of seville" overture mp3

It's exactly what I needed.