Okay the deal is simple. I lost the icons and see that white icon instead of them in the taskbar which is really annoying. Tried reinstalling Firefox, no use. (Tried checking the firefox icon in the app folder (program files), but same situation there, no icon).
OS: Windows 7 x64 up-to-date, every update installed
(Maybe related: I installed my PC with a wrong account name. Renamed it. That rename caused much headache since Windows messes with my user folder, bla bla. Now I made a new user, called "S" and I'm using this ever since that incident.)