If the television doesn't turn on, start by making sure it's plugged it; if it still doesn't turn on, check the outlet by plugging in something else. Check the circuit breaker if the outlet doesn't work.
If the TV turns on but isn't showing channels, the problem may lie with the cable box or digital receiver. Make sure the cable box is plugged in; most have a display or light that indicates that they are receiving power. Check the cables leading from the box to the television to make sure they haven't been disconnected. You can also try to unplug the cable box and plug it back it in case it has crashed.
If the cable box seems to be working, make sure the TV is set to receive video from it. Remote controls often have an "input" or "mode" button that switches between different inputs, so cycle through the options to see if the cable box comes up. If the cable box connects through a coaxial cable, try setting the TV to channel three or four.
Some people set up cable boxes through a VCR or other external device, so make sure that device is also receiving power and is attached to the television. Check by inserting a video tape or optical media; if the television plays, the problem might be internal to the cable box or digital receiver.