Well that sucks
I'm not sure if I should keep my gamecube on the old HD or the new SD. I never really noticed any input lag on the old HD anyway, but maybe that's just because I got used to it. Then again I'm very sensitive to input lag on a computer so I don't know.
However, I hooked up my ps2 to the SD TV and popped in dino crisis (a ps1) game and I don't know if it is just psychological and a placebo or not, but I thought it looked a hell of a lot better. I also noticed that I was able to corner and move my character with much more ease. The first time I played through that game on the HD I was constantly running into walls.