What are the principal components of coconut taste, and how do they differ between fresh and stale coconuts?
I don't have more than a basic knowledge of chemistry and the information I have I translated from a German book on spices and seasoning. All errors are therefore mine. The book is basically a description of a huge amount of spices, herbs and other seasonings, as well as a description of the chemistry involved which leads to the taste.

The difference in taste between coconut milk (if canned, as I assume) and fresh coconut water is easily explained. Canned coconut milk is basically a purée of coconut flesh mixed with water, which is why it has a different taste. Sadly, the book did not contain information on whether or how the flavour compounds (is that the correct word?) differ from coconut flesh to coconut water.

The book gives the following flavour compounds as responsible for the taste:

δ-Octalactone described as tasting creamy and of caramel

γ-Octalactone sweet and fatty

2-Nonanone fruity, sweet and earthy

Limonene lemon and turpentine

Responsible for the smell are the following (I have no idea what the letters and number in the parenthesis are supposed to mean, I'll simply include them):

10% Caprylic acid (C 8:0)

10% Decanoic acid (C 10:0)

50% Lauric acid (C 12:0)

15% Myristic acid (C 14:0)

10% Palmitic acid (C 16:0)

5% Oleic acid (C 18:1)

I hope this helps somehow.