Why does it have sound but a black screen?

Fault at its main digital board. Short circuited component/s at it. Contact any service technician; or the authorized service center. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts.
http://electro-medical.blogspot.com/

In most cases, the main board might have to be replaced. If so, a software [firmware] update too might be necessary.
Before going further; try a hard reset first. If it does not help you, replace the main digital board. There are two methods to reset TVs. The first is simple to do; a Hard Reset. The other is somewhat skilled; is a Factory Reset (System Reset). To make it a hard reset, just unplug the TV from AC mains wall socket, and re-plug it back after 15 minutes or so. If you do this by overnight is better. This procedure will make it a hard reset. If you want to make it a system reset [Factory Reset]; you have to enter its service mode option, and select the factory reset option. If you wish to get some details; visit the site linked here.

backlight may have gone if your tv has one

time to replace the Tv unfortunately

Despite of no image do you still have sound(happens in case of malfunctioning backlight or T-con board)?

Your color tube has probably went out that is why you have sound but no picture, you will have to call a tv repair place or where you bought it from to get an estimate on having it repaired

go to the menu and see if the set is set to high power, if so change to low power , it may make a difference ...rob

Could be the power supply gone bad.
No easy solution I'm afraid.

sounds like the lamp has shattered. check the lamp

The first step here is to isolate the problem. You need to know if it is in your TV or DVR. Unplug your TV from the DVR and connect it directly to the wall outlet. Then connect a TV antenna, or a small thin wire, to the F connector on the back of the TV (this is the threaded connector - where you plug your cable). Try searching for some air channels and see if you get any channels at all, and post back.

The horizontal output transistor drives a transformer that gives you the high voltage to light up the picture tube,either the transistor or the transformer have gone bad,sometimes both have to be replaced and sometimes the transistor fails for no reason by itself.Be safe and call for help if you are not familiar with tv service.