In Death Note, what happens to Light Yagami after he dies? I read the manga and am currently watching the anime.

Ryuk once commented that users of the Death Note can neither go to heaven nor hell. (Though one source claimed that this was only a fake rule that Ryuk wrote/spoke.)

This suggests Light becomes a Shinigami. If so, why does Light not continue the work he began on Earth? Does L (who also touched the Death Note) become a Shinigami as well, somehow preventing Light from doing his deeds?
Ryuk once commented that users of the Death Note can neither go to heaven nor hell. (Though one source claimed that this was only a fake rule that Ryuk wrote/spoke.)


No, the claim/source is incorrect. Anyone who uses/writes in the Death Note can neither go to heaven nor hell. This can be seen as Purgatory or 無 MU/Nothingness


  This suggests Light becomes a Shinigami.


Wrong. :) The rules of the Death Note have been explicitly stated in both the anime and manga as stated by Braiam which was...


  The human who uses the notebook can neither go to Heaven nor Hell and die an unfilling and unhappy life.


Finally touching the Death Note does not make you a Shinigami, although touching it allows you to see the Shinigami.