as per title captcha not showing on firefox latest version (by firefox own builtin updater). some sites require to complete a captcha to complete either registration and now for login, or it fails with the correct username/password combo. everything seems fine with IE (and probably other browsers, but not checked)
Do you have any extensions installed that could interfere with this? You can try to disable them and see if it helps.
Please insert text from about:support (NOT raw) here try safe-mode in firefox - if not working its blocked from system, otherwise extensions may cause this (see Minimalist). from my experience captures are inserted as frames by google capture service (google.com), some as flash. some may blocked, if not firefox/extension/adblocker then from possible antivirus crap. if nothing help the try to reset your profile. HTH