I'm not an expert by any means, but I'm fascinated by "Old Europe." Just by the way you worded you're question, I'm assuming you're familiar with the "Kurgan hypothesis."

Anyway, we don't know much, and everything we know comes from archeological evidence, and more controversially, oral-folk traditions. There are a multitude of pre-Indo-European cultures, but I really only know anything about Trypillian culture. It was located in modern-day Ukraine, and they give us one of the most fascinating and enduring archaeological puzzles. Every 60-80 years they would burn down their homes and villages, and then rebuild in the same area. There is no consensus, but the evidence indicates that is was not accidental.

Here is a fairly dated article, but it's very accessible and it has pictures:

http://depthome.brooklyn.cuny.edu/anthro/faculty/bankoff/burning_color.pdf