Most laptop screens are output-only (eDP/LVDS to GPU). They lack HDMI/VGA input. You cannot plug an Xbox 360 directly into a laptop screen.
HDMI carries audio. Component/VGA need separate audio: Optical (TOSLINK) from Xbox 360 → speakers/DAC, or RCA L/R from component cable → speakers.
Bottom line: Buy a $90 monitor. Capture card + laptop screen = laggy, expensive, inferior.