Many HDMI adapters are not built to handle the more esoteric aspects of older video standards, especially PAL ones and 60Hz options (which some GC stuff has as an option, or even mandated like Metroid Prime 2).
PAL things being over bright is a noted thing too. Fix on a traditional setup is to make sure the cables have a resistance of 75 Ohms which most do not (though many TVs, VCRs, scart adapters and such would ensure happens, some things even having a little switch somewhere to do it).
Most of the expensive fun video adapters people use for gaming on old stuff with modern screens will also feature this, not sure if there are simple boxes you can buy (though you might be able to do it with a trip to whatever replaced radioshack or sacrificing an old cable setup and grabbing said resistor for the yellow cable).
