I bought the sony component cable but I realized that it didn´t work because my tv has this component input: YPbPr, and the cable only works with component inputs YPbCr PrCr. So please I need someone who can help me to explain if there´s a way to play my PS2 in a Sony bravia Full Hd with component input YPbPr.

Does it not have a composite or SCART? if so I'd suggest that but it looks a bit like it's time to upgrade to a new PS3. Or buy a lesser TV
To be honest a decent HDTV will really show up the last gen consoles. You can get component cables for the PS but i'm not sure that the PS2 will recognise them I'm afraid.
Sorry but it's time to upgrade your console