Before the spread of the Indo-europeans, which I am not going to specifically talk about because we still dont specifically exactly how that happened, there was a "Old Europe". It was in all likeliness a hugely complex and diverse prehistoric world. While some archeologists such as Marija Gimbutas believe there was a unified old european language, if you look at the known pre-indoeuropean substrates in many later languages you can see there was a lot of diversity in the languages.

Some of these substrates are present in Germanic languages: https://www.academia.edu/3755296/Is_There_a_Possibility_to_Find_Substrate_in_the_Germanic_Lexicon

As well as Vasconic languges: http://vernaculum.files.wordpress.com/2011/10/rebecca-5.pdf

There is also a hypothesized linguistic group in what is not the Netherlands and Belgium, called the "Nordwestblock" that was overcome by indo-european Celts and Germans right around the Gallic wars.

I have to state a great deal of this is theoretical, and many of these subjects are under heavy debate by academics(such as the Germanic substrate and the Nordwestblock)

Another sign of the pre-indo European peoples of Europe is in river names. Here are three maps with rivers with known pre-indo-european roots: http://en.wikipedia.org/wiki/Old_European_hydronymy#mediaviewer/File:Krahe.jpg

http://en.wikipedia.org/wiki/Old_European_hydronymy#mediaviewer/File:Hidronimia3.jpg

http://en.wikipedia.org/wiki/Old_European_hydronymy#mediaviewer/File:Krahe-2.jpg

Genetically I say a great deal, although studies have shown that the Neolithic peoples of Europe recieved to varying degrees Near Eastern genetic traits, such as the haplogroup J2, linked to Anatolian populations. These genetic markers still exist in Europe, primarily in the Mediterranean parts of Europe.

As for the Minoans, we have little written evidence of Minoan language, with the exception of some hieroglyphs. There is a theory that the Eteocretan language from later times is related to the Minoan language but we dont know for sure. Personally, I think based on the Minoan roots in the Neolithic Near East that their language would have been a relative of the oldest Non-indo european languages of southern Anatolia who are themselves relative of the Hattic language encountered by the first Hittites circa 1700 BC. It is almost certain however that the Minoan language was non-indo european.