Installing Firefox and running defrag don't require the removal of anything.. A little more information would sure help.. Are you running Windows 8 or Windows 8.1? Are you able to get on the internet with your browsers? (You didn't tell us which computer you're using to post this message.) Why do you think you may have removed something? Did you delete files and if so, which ones? Are you able to download files using Internet Explorer?
And just in case you have a problem with malware, please click on the link below and follow the steps to the letter. In order to download the removal tools, you'll probably need to use a separate, clean computer to download the files, then copy them to a CD or flash drive, then transfer them to the problem machine.
“Expand” the post titled: "Please try this" at the link below:
http://www.cnet.com/forums/post/f742c795-5881-433b-a29b-6d758efe5cd3/
Hope this helps and let us know what you find.
Grif
I have windows 8, and am using Firefox. My internet connection is via satellite. I recently updated to newer Firefox and did a disk defragmentation and may have removed something important unknowingly. I cannot download anything at all, not even my AVG updates. I have tried to refresh Firefox, that didn't do anything. Hope someone out there can help me out.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic