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GuyZ

We'll be releasing one soon!
Thanks! We think so too :)!
(Enigma here). Yes, that is possible. You can distribute a key to the nodes and make it retrievable only if some computation is satisfied (which is also done privately and leaks no information).

We have some ideas on how to do it, but we're hoping gifted developers out there would use our platform to develop such highly-needed applications (that would probably be much better than what we have in mind).

One of Enigma's creators here. Indeed, that's a very prominent application that is one of many to motivate our work!
The idea is for the owner of the data to share her own data into the network. There could be many owners for different pieces of data.
This is actually a form of encryption (See - https://en.wikipedia.org/wiki/Threshold_cryptosystem). It is encrypted in the sense that combining any number of pieces smaller than the defined threshold won't leak even a single bit of information.
(I'm one of the creators of this project)

I don't believe centralized/public clouds will disappear anytime soon. However, there simply aren't any privacy-preserving alternatives out there. We're hoping to change that.

Also, your description is accurate. We'll be releasing our code and some dev-friendly documentation for the beta soon. You're welcome to sign up at http://enigma.media.mit.edu.