If your set is supposed to be "1080p" then it will accept a 1080p signal coming in from something like a PS3. If it is having problems I would check the settings in both the set and the source.
It is my understanding that you cannot send 1080p over component cables and should be using HDMI for this signal.
Does it matter if an LCD has 1080p resolution if the video inputs do not accept 1080p? I am not understanding the value if the television cannot receive 1080p input from a ps3, etc. I'm probably missing something... any help?