Are there any bitcoin node that are running the original Satoshi codebase? I was taking a look at all the different kinds of nodes running bitcoin. Are there any nodes that are verfiably running the original Satoshi client so that we can confirm backwards compatibility?

If not, what is the oldest operational bitcoin node?
If you mean truly unmodified, the answer is almost certainly no.

Version v0.2.9, released on May 26 2010, introduced checksums in the protocol. During a transition phase until Feb 20 2012, checksums were only used after a version negotiation, making sure both parties understand checksum. After Feb 20 2012, all new initial connections would start using checksums everywhere. This transition period was designed by Satoshi, and took effect on the planned date without any issues.

However, it means that no Bitcoin software from before May 2010 is currently compatible with the existing protocol. It is however possible to write protocol adaptors, or make small patches to old code to make it function. With such changes, version 0.1.0 should accept the current blockchain.