Television and Home Theater

I have a Mitsubishi VS-5042 50" rear projection that is about 10 years old with low to moderate use.  Of late the picture is not as crisp and clear.  My kids call it "kinda fuzzy."  Especially print or lettering.  A bit "out of focus" if you will.  Attempts via the color adjustment and color "Alignment" don't seem to help.  Any ideas?

The cable hookup plug broke off clean. It's a 54 inch 2002 big screen phillips/magnavox. How can I repair it?  Please help my little ones like to watch wttw. I have no picture at all since the plug came out.

i have a rca 27 inch tv in my bedroom.  model # F27664.  up until now, it's worked just fine.  last week the picture was good, but the speakers didn't work.  i took the back off and blew out all the dust, put it back together, it worked fine until today.  i took the back off again, but, now i have to plug and unplug it from the wall to make the speakers work.  when i plug it in, it'll work about 7 seconds.  picture stays on, no volume.  can you help me?