CAPTCHA image verification not showing/the website does not supply identity information/your connection to the site is only partially encrypted

CAPTCHA's are accomplished with cookies.
Try this:
For Firefox, configure this first:
Tools> Options> Privacy: top drop menu set to "Firefox will use custom settings..."> Check 'Accept Cookies from sites' 
?Un-Check 'Accept 3rd Party cookies'
Go to the site needing cookies> copy that URL> Tools> options> Privacy> Exceptions> (paste that URL into slot)> Allow> Close.
This small utility will assist managing (allow/disallow) cookies on a "site-by-site" basis:
Cookie Button 0.9.3: https://addons.mozilla.org/en-US/firefox…

"NoScript' users may have to "temporarily allow....." from the blue 'S' tray icon. 
Supplemental blockers, in browsers mainly, may have to be muted, or 'site allowed'.
No need to relax any other cookie settings (which help deter junk ads, pop-ups', malware etc.):

Internet Explorer users, do this first (IE, pre-8, should NOT be used: to many 'broken' security aspects):
Tools> Internet options> Security> tick the "Internet" icon> Security level box> set slider to "Medium high"> OK out. 
Then:
Go to the site needing approval & copy the URL from address bar, then:
Tools> Internet Options> Privacy> Sites> paste that URL into top line> Allow> OK> OK.
The "Pop-up Blocker" may also need to be modified to accommodate the site. 
Tools> Internet Options> Pop up blocker heading> Settings> repeat URL pasting into the slot> Close> OK.

General cookie settings should be:
Tools> Internet Options> Privacy> Advanced: tick "Override..."; Allow 1st party cookies; 
Allow session Cookies ?BLOCK 3rd Party cookies> OK> OK.