CureCoin is the coin that is closer to this project. I have been thinking a lot about the distributed computing cryptocoin. From distributed storage (torrent, datacoin, and more to come), distributed CPU, GPU, broadband, etc.

Curecoin uses a centralized pool to send processes to the miners, and has a rare reward system. The user should adquire the processing power paying in the same coin, ie. curecoin.

I think the first steep in this kind of coins would be with mathematical calculus or simulations, like finding solutions for mathematical systems or something like that. We should find a way to probe the work that is done by the node, that´s critical.
In particular in the subject of distributed storage cryptocoin I know a developer who have some ideas on how to make the Proof of Storage.

I´m would like to participate in a team developing this distributed computing coins, as they are going to be bigger that the big guys servers.

May be just a cryptocoin with an integrated chat system and you can rent chat time / words in cryptos.

It uses a proof of stock-- instead of incentivzing for mining power, it invcentivizes for computer space provided.  At least I think this is the vision for how it will work. 
My thoughts are  because this is based on storage space-- proof of stock-- this would be that datacoins value will only appreciate with the costs of storage space.  The cost for storing data in the blockchain will continue decreasing.  Meaning the cost of mining datacoins will depreciate also.  This means that datacoins won't really appreciate in value.  At least not astronomically.  The cost of datacoins is the cost of storing in the blockchain.  Since this is a Distributed Automnomous Corporation, ots essentially the cost of buying an application/ software.  This cost (storage space) should decrease over time....   What do you think?  Anything else you can add.   

I'm very concerned about the realms of putting illegal material into the blockchain.  We as a cyptocurrency community should limit attention to ourselves-- especially when we want bitcoin seen favourably in the publics eye

I already talked about this with some friends. Proof of Storage.

You will hold encrypted chunks of data. The network must send you some kind of request that you could only solve if you hold the corresponding chunks.

Amazon S3 fear this!