If you are actually using a component cable (3 or 5 connectors with 2 more for audio) then you should be able to do HD signals unless your capture device or source device is limiting you. Based on the SD resolution limit, it sounds like you may actually be using a composite cable though (1 yellow cable for video and a white and red cable for audio). Composite cables only go up to SD resolution (more accurately 720 by 480 for NTSC and I forget the exact resolution for PAL but it is 576 horizontal lines.)
If you want to record HD videos using your PC you will need an actual HD capture device. I'd personally recommend going with something HDMI based since your camera supports HDMI out. This would prevent quality loss from going to analog and back to digital (component video cables are still analog). Such devices aren't super cheap though. Devices like the Black Magic Intensity or Matrox MX02 will handle your needs, but they are in the $200 price range.