If there are multiple component inputs check that the one you're hooking up to supports HDTV. You mention the "P component" as if there are more - chances are the "P" one is for HDTV (480p/720p/1080i).

If you have a standard DVD player it should work through the normal component input (assuming there is one that only takes 480i signals). If it's progressive scan, try turning that feature off (you may not need it).

DVI/HDCP would be the highest quality way to get HD to your set.