Video works but no sound

Check its power regulator board for faulty component. It will be best to replace it as card basis.

There are two places to look for the problems, the backlight inverter board and the power supply. Look at the power supply first since it is easier to get to, look for burnt parts, bad capacitors, etc.
http://en.wikipedia.org/wiki/Capacitor_plague
Please post back what you find.

If there is no picture, just black screen.. then the cold cathode (backlight) on your monitor is busted. Or its ballast transformer is burnt out. Replace it to work again.

you have a bad master and slave inverter board these are the skinny boards that go verical on the back of the unit
take you unit apart remove back and look at the back of the tv face down on a blanket remove all the screens take the back off remove those two board going vertical look up both parts on google or call or go to shopjimmys.com

If the fuse burned out the the tv would not turn on at all. When the tv is on is the back light still on? If its not its probably the back light that needs changing. If its on then its one of the circuit boards.

Hi, I had a computer monitor that acted similar one time and what I found were that there were some bad capacitors in the power supply board inside. They were identified by the swelled up rounded ends and the heat discoloration of them. They look like little aluminum cans with a vinyl sleeve shrunk around them with the component values written on them. A normal one is flat on the end with no signs of any leakage around them of a brownish blackish substance similar to wax or tar. They are relatively inexpensive at an electronics supply store($1-2 each) so I replaced them all. This will require some soldering and electronic repair knowledge though. The power supply could not stabilize so it just kept shutting down the picture that only displayed for a brief instant.
Good Luck!

Turn down the Bass level in the sound option and turn off and sound options that you don't need.

Try plugging in a powered antenna.  
The DTV coax input is for over-the-air HDTV transmissions which vary depending on your location and surrounding buildings.  I have the LCT32HA36 hooked up to a powered antenna and it works fine, but it wouldn't work when I plugged in the cable from the wall.

What resolution are you using?  It might not work if it's set any higher than 1366x768.  And set the refresh rate to 60 Hz.