Eurostar's technical problems explained identifies the cause of the train failures as fine snow getting onto electrical equipment and melting. However, this problem has been known since 1982, according to the article.
According to some passengers on at least one of the trains, there was something like an explosion just before the train stopped. This is consistent with another potential cause (which I mentioned in a previous entry), which is essentially that ice builds up under the trains and falls off in large chunks when it warms up in the tunnel, potentially damaging electrical connections.
I don't buy the notion that moisture brought the trains to a halt. If it was known that this was a possibility, then I would expect them to have designed a solution long ago, or to at least have a plan, and the capability, to rescue the passengers, instead of locking them in the train with the apparent intent of leaving them until they started dying, and not even telling them what was going on. It is this treatment, which smacks of sadism/SRA, which has me smelling an evil rat.