It's possible it's an issue with the signal option not being set (Japanese GCNs output a different signal than UK or NTSC GCNs and this will need to be set in your devices settings. It's the list of settings that is like NTSC_M, NTSC_433, PAL_B, etc.
Do you have any other SD console you can test? Maybe a US or UK GCN?
Also, are you using RECentral or LGP Stream Engine as a source?
If I remember right GCN's AV cable is component, right? Did you make sure to switch to component in REcentral / Stream engine?
Avermedia doesnt take Composite Video (Yellow Cable), you need Component (Red Green Blue).
That's strange...
I play my RE2 (USA-version) on a chipped japanese Gamecube, and my Elgato HD have no problem grabbing the signal. Hope you'll find a solution.
EDIT: Oh yeah, and I only use AV-cables.