We need to invent a verb for this that is used the same way starve would be used. 
Thirsted to death is not bad but the parallel for food would be hungered to death, not 
starved to death, so it is not ideal. Starve is a verb used to indicate not just hunger but it also indicates that some damage is taking place to the body, the body wastes away. 
Someone suggested "death by desiccation".  Like starvation, it also is a slow process so how about "He desiccated to death. However, I think this is closer but still not ideal, as desiccation focuses on the end state, while starvation focuses on the suffering process. A word that focuses on the process would be dehydrate.  So "he dehydrated to death" might work.  What do you think?  Sounds too strange?