Why isn't Mozilla Firefox connecing to any websites, but Internet Explorer is?

It all started when I deleted Norton Anti-Virus from my computer before downloading McAfee. When I went to download McAfee, it said it could not connect to the internet, even though I had gotten to that point through the internet using Internet Explorer. However, Firefox could not connect to any websites. I tried a System Restore, restarting my computer, reinstalling Firefox, but I still get the same message when I try to download McAfee, and Firefox will still not connect to any websites.

I doubt this is a malware issue.
Uninstall Firefox again.

Firefox leaves behind it's folders when uninstalled, so locate and delete these two folders. One of them is hidden, so hidden files need to be shown.

1. Open My Computer.
   
2. Go to Tools > Folder Options.
   
3. Select the View tab.
   
4. Scroll down to Hidden files and folders.
   
5. Select Show hidden files and folders.
   
6. Uncheck (untick) Hide extensions of known file types.
   
7. Uncheck (untick) Hide protected operating system files (Recommended).
   
8. Click Yes when prompted.
   
9. Click OK.
   
10. Close My Computer.

Locate and delete these two folders:
C:\Program Files\Mozilla Firefox
C:\Documents and Settings\[USERNAME]\Application Data\Mozilla

Re-install Mozilla Firefox now.