We study the questions of the existence and mass of the proposed $d' (IJ^P=00^-)$ dibaryon in the quark-delocalization, color-screening model (QDCSM). The transformation between physical and symmetry bases has been extended to the cases beyond the SU(2) orbital symmetry. Using parameters fixed by baryon properties and $NN$ scattering, we find a mild attraction in the $IJ^P=00^-$ channel, but it is not strong enough to form a deeply bound state as proposed for the $d'$ state. Nor does the (isospin) I=2 N$\Delta$ configuration have a deeply bound state. These results show that if a narrow dibaryon $d'$ state does exist, it must have a more complicated structure.