The "Dark Ages" are a bit of a myth; the concept was invented by historians in the 18-19th centuries, and the tag stuck. It wasn't so black and white, and science didn't stagnate as it does in the graph. Wiki:The medieval period is frequently caricatured as supposedly a "time of ignorance and superstition" which placed "the word of religious authorities over personal experience and rational activity."
Actually, reason was generally held in high regard during the Middle Ages. The historian of science Edward Grant, writes that "If revolutionary rational thoughts were expressed [in the 18th century], they were only made possible because of the long medieval tradition that established the use of reason as one of the most important of human activities". Also, contrary to common belief, David Lindberg says "the late medieval scholar rarely experienced the coercive power of the church and would have regarded himself as free (particularly in the natural sciences) to follow reason and observation wherever they led".
Other misconceptions such as: "the Church prohibited autopsies and dissections during the Middle Ages", "the rise of Christianity killed off ancient science", and "the medieval Christian church suppressed the growth of natural philosophy", are all cited by Ronald Numbers as examples of widely popular myths that still pass as historical truth, although they are not supported by current historical research
And talking about universities:The first universities (University of Bologna (1088), Paris (teach. mid-11th century, recogn. 1150), Oxford (teach. 1096, recogn. 1167), Modena (1175), University of Palencia (1208), Cambridge (1209), Padua (1222), Toulouse (1229), Orleans (1235) began as private corporations of teachers and their pupils.
So three hundred years before the Renaissance, universities were being established across Europe. Sure, the Church was involved, but the principle of secular education and science was established then.
It seems pointless to ask where science would be without religion. Religion was a crucial aspect of mankind's development; its early appearence, ubiquity and longevity testify to that. Without it we might still be living in caves.