You did everything. Tried uninstallers, antimalwares, deleted files and folders, removed toolbars and search box named "Search".
(While search boxes are named "google", "bing", they named it generically "search", quite short of questioning the intention behind.)
But when you use firefox web home page search box, you are still automatically redirected to funmood's search results.
They have named it a fantastic malware that used funmood. Others just dismissed it as only PUP but totally annoying. It depends on what funmood you have installed and from where.
Do two steps below if you want to completely remove it (with the bonus of not uninstalling and removing all your firefox addons and plugins)
FIRST, mozilla told to start firefox in safemode. For version 11 look for safemode in the browser's help tab, click it and the browser will restart.
BUT SECONDLY (this is the most important and I have not found anywhere), check all the boxes to be checked to make safemode permanent and then continue.
That's it. You have to test the home page search box again of firefox to see that you will no longer be redirected again to funmood.
You can add your plug ins, themes, and add ons one at a time while testing if it will not cause a redirect just to be sure. Or you can do it by batch for the ones that you're sure are not causing the redirect.
Praised be Jesus and Mary.