The problem is that you're blitting to a window handle and not to a image handle.
do something like...
SourceWindow=WindowCreate(10,10,SourceImageWidth,SourceImageHeight,"Source Image");
int SrcWinImg=WindowGetImage(SourceWindow);
Blit(0,0,SourceImage,SrcWinImage);
ShowPage();
Haven't tried it cause my comp is kinda in limbo, but it should work.
Also this business about doing WindowHide(GameWindow) strikes me as rather odd o_O