I am thinking about the difference between the usage of "dead eyes" and "the eyes of death". Can someone enlighten me.
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The usage of the eyes of death is a metaphor for death itself. (To be precise it's a synecdoche, in which the part stands in for the whole.) Consider Northumberland's declaration from Shakespeare's Richard II (Act 2, Scene 1):
even through the hollow eyes of death, I spy life peering
That is, in the midst of death, life still shows itself.
Or from Byron's Mazeppa
And my dim eyes of death had need.
No hope arose of being freed.
The protagonist is near death and needs rescue, but he is without hope of such.
The eyes of death may be described by other adjectives such as fearful and ruined, but these are depictions of death more than the the look in someone's eyes.
The term dead eyes finds two uses. The first is to characterize a corpse through the stillness and unfocused nature of its eyes. The second is to describe the look of someone without compassion or indeed any feeling at all. From Black Magic: A Modern Arabic Novel by Hamdy el-Gazzar (emphasis mine):
She doesn't believe in symbols and she's not horrified by the look in your eyes, your dead eyes, empty of all expression, of everything.