If I own a music CD and I rip the songs to my computer as a backup
copy and the disc is destroyed, would it be legal to sell these songs
(under U.S. law) individually?  If so, why and what law states so?  If
not, why and what law prevents this?

No. Many people frequently confuse the concept of "fair use" and
believe that as long as they are not profiting from copies of
copyrighted material, their conduct is legal. This is not accurate.
Although it is true that the unauthorized copying, public performance
and distribution of copyrighted musical material for profit is almost
always an infringement, it is not true that the absence of a profit
motive eliminates the possibility of infringement. The "free of
charge" copying and distribution of music by consumers comes at a
significant cost to artists, writers and musicians ? namely, lost
sales based on the dissemination of free copies. It is almost always
the case that the distribution of unauthorized copies of musical
recordings ? even if to your friends and even if for free ?
constitutes copyright infringement and is not a "fair use."

Fair Use Rule Definition :
the fair-use rule is a privilege in others than the owner of the
copyright to use the copyrighted material in a reasonable manner
without his consent. The reasonableness of a use is determined on a
case-by-case basis applying an equitable rule of reason analysis.

So to answer your question, making a profit from someone else's
Intellectual Property, without the owners consent is illigal.

View this link for the Copyright laws that restrict you from doing this.
http://www.sls.lib.il.us/reference/workshop/suite6.html