I don't know any coins that operate without either Proof-of-work or Proof-of-Stake. To make your ideal a reality someone would have to invent a new way to power a block chain, unless I missed a coin that quietly implemented a new system without many people noticing.
I have such technology under development.
so you wanna be funded?
you may wanna just join a team instead and with their existing coin if possible, you wouldn't need more funds but just an update to the coin. and you still have the legacy still.