This is Charon, and he ferries the souls of the dead across the River Acheron. Hey, it's a living. (Or something.)
If you click on his left hand, he opens it, and Nancy says that he needs something before he'll take you across the river. There's more information about this in the museum office.
In the Messenger program on the computer, Melina says Charon needs a coin, and it has to be a replica.
Also, one of the red notebooks in the cupboard includes a note from Melina that all the coins in the display are replicas because the real ones are stuck in customs.
So go to the coin display and take one of the coins. Put it in Charon's hand, and he'll take you back and forth from now on.
How do I get a key for the coins display?