Ancient Cretans were of Anatolian origin.

New paper (abstract only for non-subscribers) on ancient Greek DNA: R.J. King et al., Differential Y-chromosome Anatolian Influences on the Greek and Cretan Neolithic, Annals of Human Genetics, 2008.

Abstract:

The earliest Neolithic sites of Europe are located in Crete and mainland Greece. A debate persists concerning whether these farmers originated in neighboring Anatolia and the role of maritime colonization. To address these issues 171 samples were collected from areas near three known early Neolithic settlements in Greece together with 193 samples from Crete. An analysis of Y-chromosome haplogroups determined that the samples from the Greek Neolithic sites showed strong affinity to Balkan data, while Crete shows affinity with central/Mediterranean Anatolia. Haplogroup J2b-M12 was frequent in Thessaly and Greek Macedonia while haplogroup J2a-M410 was scarce. Alternatively, Crete, like Anatolia showed a high frequency of J2a-M410 and a low frequency of J2b-M12. This dichotomy parallels archaeobotanical evidence, specifically that while bread wheat (Triticum aestivum) is known from Neolithic Anatolia, Crete and southern Italy; it is absent from earliest Neolithic Greece. The expansion time of YSTR variation for haplogroup E3b1a2-V13, in the Peloponnese was consistent with an indigenous Mesolithic presence. In turn, two distinctive haplogroups, J2a1h-M319 and J2a1b1-M92, have demographic properties consistent with Bronze Age expansions in Crete, arguably from NW/W Anatolia and Syro-Palestine, while a later mainland (Mycenaean) contribution to Crete is indicated by relative frequencies of V13.

I have marked in bold type the two more important passages:

1. Ancient continental Greeks (or rather pre-Greeks, Indoeuropeization didn't begin till the late part of the the3rd milennium BCE) were, in full accordance with the archaeological data, related to other Balcanic peoples of the time (Balcanic Neolithic). Instead, more mysterious Cretans (Eteocretans) have an Anatolian origin, connecting them with other pre-Indoeuropean peoples of the area like the Hatti or possibly ancient Troy.

2. Greek E3b1a2, that relates to North and East African (but also West Asian) clades of the same lineage, is not Neolithic but older. That basically excludes its arrival by boat and means it must have gone via West Asia. This raises more incognites than anwers actually but, well, it's possible, that Neolithic population movements in West Asia reshaped the genetical landscape, leaving E clades in a less prominent position, or maybe the high presence of E3b in mainland Greece and nearby areas is due to some founder effect.

What I wonder now is how long it will take since these findings until Linear A is deciphered. The linguistic keys for the Eteocretan language are more apparent now: either Hattic (arguably a NW Caucasian language) or Etruscan-Lemnian (a well documented isolate) could well be relatives of the language of the Minoans. Of course it's a complex matter and I may be adventuring too much here, but so far most attempts seem to have been oriented towards shallow connections with either Indoeuropean (Greek, Hittite) or Semitic languages, what is a fundamental nonsense.