I have an element flat screen ELDHW421 I have the caption in the menu screen turned off, but the closed caption will not go off.

SOURCE: closed caption and black square

your TV do not disable close caption in composite mode. It may in component mode. Please make sure that the close caption in your TV menu is not set to "text"
Please be advice that CC :Text is the ONLY one that can give you a black box.

Best regards
Circuitcity

SOURCE: Sony 46" XBR2 Cannot turn off closed caption

With TV on, turn off DVR and hit menu on DVR remote - you can disable CC from there.  Worked for us - got the idea from another fixya post. 

SOURCE: closed caption problem

I had the same issue... here's what I did.  If power off your cable box, then press the menu button, there's a selection to enable or disable Closed Captioning.  This works for both HD series Motorola boxes Comcast offers, at least in the Minneapolis/St. Paul area.  Hope this helps!
Evan

SOURCE: toshiba 62hx94 cant shut off closed caption have comcast cable

The problem was with the Motorfolla Comcast cable box not my T.V. . I turned off my Comcast cable box, pressed menu on the remote to the cable box. This made a 16:9 ratio appear on the cable box's LED read out, and a bluish screen appear on my television. One of the options on my television was to turn on and off closed captioning. Therfore, I turned off closed captioning and the problem was solved.

SOURCE: Close captioning on HDMI

The TV will not display closed caption with HDMI input. It must either over-the-air (antenna) or composite input for the TV to manage CC.

To get CC with HDMI from your Comcast DVR, you need to configure the cable box. Instructions can be found here:
http://en.wikibooks.org/wiki/How_to_use_a_Motorola_DVR/Setup

If you want CC all of the time, this works well. But since you must power-off the cable box to change the setting, switching CC on and off is a real pain.

Your set-up is similar to mine (Sharp Aquos 46" and Comcast DVR). I have the composite output from the cable box going to a DVD-recorder and on to the TV. Whenever I need CC (usually to catch some mumbled dialog), I just rewind the DVR, and switch the TV input to the composite input. Then I switch back to HDMI to continue watching in HD.