Try turning off the 360 by the switch on the back of the box; then on the front of the 360 box hold down both the standby/power button and the - (minus) button at the same time. Then turn on the 360 again whilst keeping hold of those buttons for a further 30 seconds.
If the standby/power button and the - button workaround doesn't solve it then try using the standby/power button and the + (plus) button at the same time instead.
You could also try the three fingered salute, which is switch off on the back of the box; then on the front hold down the plus, minus and standby/power buttons at the same time, and switch on again whilst keeping all three buttons pressed down. When it restarts you might see a message it can't acquire the channels. If so press OK and let it restart again.