In greek mythology the name of the man who cannot reach food to eat?

Tantalus, whose name is the origin of the Word "tantalize".

He served the gods his son as the main course of dinner, and for that was damned to eternal starvation and thirst.

I think that was him- it might have been Sisyphus. The story, not the punishment; Sisyphus was doomed to roll a rock up a hill forever.