Although it's possible to repair some parts of a broken flat-screen TV, it isn't cost-effective, and some parts, including the screen itself, cannot be easily repaired at home. Because flat screen TVs employ a layer of pixels with a layer of plasma beneath it, they aren't easy to fix.
If the glass is cracked, it's possible to replace the screen; doing so could cost several hundred dollars. Deeper damage than the screen cover costs more to repair, often more than it costs simply to replace the TV. If the TV doesn't work and there is no apparent exterior damage, the problem probably lies with the electronics. While it's possible to replace capacitors and diodes, working with unfamiliar electronics can be dangerous for those unfamiliar with the system.