It is difficult to give you an accurate answer as there are so many things involved.
If you were getting a good TV signal before digital then there is every chance the aerial you have will pull in a reasonable digital signal.
The trouble can start from there. You must have good quality quad shield coax cable all the way from the aerial to the back of the TV. Old coax cable used with analogue TV won't do it for you. Even a short length of old cable can ruin the signal.
Then, you might need a digital signal amp if the cable has been split anywhere to different rooms.
It is possible on your TV to display 2 coloured bars, one to indicate signal strength and the other signal quality. They are not graduated with numbers, but should generally be about 3/4 along minimum for a decent picture. You can therefore see what is wrong in a gross way.
See p122 here http://downloadcenter.samsung.com/content/UM/201201/20120128144251913/LX5ATSCA_LX9ATSCA_ENG_US.pdf
and
https://www.youtube.com/watch?v=JWFteLOroSwhttps://www.youtube.com/watch?v=TzHgKh9Xqnw
it could be a backlight problem. Try this, dim the lights in the room, turn the set on. Take a bright flashlight and shine it on the screen. If you see a faint image on the panel, you have a backlight fault.
You first have to find out the panel model # of your set. Sometimes a particular TV model will come in multiple configurations with different panels. The cheapest place to look is EBay or retechtvparts.com. Beware that a replacement panel can cost you more than a new set!
back - light problem. Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis. http://electronicshelponline.blogspot.com/ To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement. To some models sets, the back-light inverter and SMPS section circuit will be integrated at its main board itself. If so; the main board should be replaced. To some models of sets, all these section circuit will be integrated at its main board. If this is the case, you have to replace the main board.
Caps can fail with no outward signs. It takes a special meter to test them. Your set may have a back light inverter that powers the back lights. When it fails, the picture cant be seen, but you have sound, to check this look for a picture on the screen using a flashlight
Back - light problem. Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis.
http://electro-medical.blogspot.com/http://electronicshelponline.blogspot.com/
To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement. To some models sets, the back-light inverter and SMPS section circuit will be integrated at its main board itself. If so; the main board should be replaced.