first, make sure your laptop can output the native res of a 24" monitor (1920x1200 or 1920x1080).

as for the split-screen effect, this app *may* do it.
http://virt-dimension.sourceforge.net/
also look at the other apps in this article: http://news.cnet.com/8301-13880_3-9902461-68.html

if your laptop uses ati or nvidia graphics, consider using their desktop managers. both should allow you to pre-size app windows to mimic a split screen (the browser automatically opens on the left side, email automatically opens on the right half).