The Gamecube on a good day can only output 720x480p, but not even all games support this. Seeing as you're using a normal composite video cable, you're using 480i, but the quality will be even more degraded due to the input type. Heck, on my old SDTV there is clear difference between composite and s-video, so I can only imagine how bad it looks on your 1400x900 display.
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