I believe it comes from the term 'deduced' reckoning or 'deduced' position which would be abbreviated to "de'd" in the Log and when spoken gives 'dead'.
At least I don't think so. Its often been claimed on this board, but I've never heard that before.
The OED (from memory) gives 'dead reckoning' as first appearing in the early C17th, following the appearance of 'dead' meaning accurate, as in 'dead shot', about 20 years previously.
DR was a big advance when introduced, but ironically most people now think of it as the least accurate method of navigation.