I could see the FireFox process in the Object Browser panel. The problem is --only Window level replay and object recognition is working. With in the window --dropdown etc. controle not recognized at all.
Currently, Firefox 3.6 is not supported. Support for this version will be included in the next major version of our product - TestComplete 8.
TC 8 is in the beta testing stage now. It will be released within a month or so.