Disclaimer: Not a historian, but Greek. I'm not sure what you're referring to as "Dark Ages of Greece", but I'm guessing you're talking about the European Middle ages (approximately the 5th to 15th century) and not about the Bronze Age dark ages of 1000 BC.

In contrast to the western part of Europe, where there was a sort of cultural cull until the Renaissance, the Byzantine empire, a continuation of the Roman empire, flourished in the Greek and Middle East region until the 15th century.

Even though for the first centuries Latin was considered to be the official language, Greek was more widely used in the region and was eventually adopted as the official language of the empire.

Even after the fall of the Byzantines and the rise of the Ottoman empire, Greek variations continued to be the lingua franca in the Greek and Middle East region, and on those variations, the official language of the Greek State was based.

Not sure if I accurately answered your question, but in essence, people in the Greek peninsula didn't stop speaking and writing in Greek at some point, but rather continued using it despite being a part of other empires.