Why won't my computer download anything-specifically the latest version of iTunes?

There are many reasons computers won't download. Try resetting Internet Explorer. To do that, go to TOOLS | INTERNET OPTIONS. On IE 7 and 8, you then click on the ADVANCED tab and click RESET. On earlier versions of IE, it's under the PROGRAMS tab, I think (I forget).

If you can't download after that, there may be a strong possibility that your computer is infected with a computer virus or other form of Malware.