Well I did a bit of research and it seems that white squares with DirectX 7 it's pretty normal event. Another important thing is that the AVG antivirus may cause problems and the only way to get rid of them is to uninstall the AVG. I did so and in effect problems are muchmore less frequent. So...
When I run Half-Life 2 with:
DirectX 9
-It crashes when background animation is loaded
-If it does not crash when background animation is loaded it crashes during a level loading process
-The consequence of a crash is that "No video input" appears at my monitor and the only option is to...