Do you get the black screen with different inputs? Cable or satellite box, over-the-air antenna, DVD player, game box? If it's only one of those, that's where the problem is.
If it's with everything, then you have an interesting problem. Your video circuits are mostly intact if you get the menu screen okay--it's the incoming signal processors that are not cooperating. That's fixable, but it would require a trip to the repair shop, and you may find it better to replace that inexpensive TV rather than repair it
