  We define the singular orbifold elliptic genus and $E$-function for all
normal surfaces without strictly log-canonical singularities, and prove the
analogue of the McKay correspondence in this setting. Our invariants generalize
the stringy invariants defined by Willem Veys for this class of singularities.
We show that the ability to define these invariants is closely linked to
rigidity phenomena associated to the elliptic genus.

Algebraic Geometry