I would like to know how many BTC have not moved from the block they were mined in - never transferred or spent. (With this information I believe could have an idea of how many BTC have been lost). Is there a tool to see this kind of information?
I don't think your question quite makes sense. Bitcoins aren't "transmitted", they simply sit in the block chain until someone chooses to spend them. There's no way to tell if a particular Bitcoin is lost or not because that depends on whether anyone knows they key needed to claim it. That key could be written on a piece of paper for all we know.
When your client tells you that you have 50 Bitcoins, it is doing that in a purely passive way. Nobody can tell that your wallet contains the keys needed to claim those Bitcoins, and this is by intentional design.
You could fairly easily measure how many coins hadn't been spent since they were mined. But that wouldn't really tell you anything. Some of those coins may have lost keys and some may not. And some coins may have been spent once and then lost.
I don't believe anyone has compiled the information but you could obtain it all from block explorer.
You would need to go through block chain and record the signing destination of all 144,667 blocks.
These are the "original" (as of today) 144,667 blocks. With a list of them you could simply scan the block chain to look for at least one transaction (other than signing transaction) involving that address.
A couple of issues: a) like David said above just because it hasn't been spent doesn't mean it is lost (unrecoverable). Many of the early adopters racked up hundreds of thousands of bitcoin. Highly probable that many of them are still accessible and simply haven't been transferred.
b) second issue is the existence of pools. With mining pool there will always be one transfer. From the pool to pool member.