The way to have 0s or background values ignored is to create a mask of the areas you want ignored.  The mask can be created from a vector or ROI or you can simply set a data range in the mask tool.  This tool is found under Basic Tools ->Masking->Build Mask.  Once the appropriate mask is created, then when you select your data file in the Classification file selection dialog you also have the option of selecting a mask band.  ENVI will use the mask band to exclude pixels from the classification.