Beginner Level Solution - Cable Check
The simplest, and most obvious, solution for this kind of problem is to check the connectors to the LCD TV in order to make sure that the connectors aren't the issue that's causing a blank picture. For instance, if you're using the connectors on the back of the TV with a splitter, there's a chance that the picture might go black if you should decide to use both devices at the same time, or occasionally, one device at a time if there's an incompatibility in the system.
As a rule of thumb for checking connectors on a system like this, you should take a great motto from building PC hardware and troubleshooting problems on there. Simplify, simplify, simplify, and remove. When you have the bare-bones system running, that should give a clearer indication of usually either 1 or 2 possible places where there is a problem.
For instance, with a TV set up with multiple peripherals connected onto the TV, you should narrow the problem down to the TV and a peripheral in question until either the TV or the peripheral work alone. In terms of a blank screen problem, the issue usually lies with the TV itself not the other equipment.