You left your birds alone for so long with not enough food, with "not a husk left" by the time you returned as you say, and are still wondering why they died???
Shockingly irresponsible, I'd say!
Any finch book written for beginners would start by saying that if you can't ensure your birds will be looked after properly during your holidays etc, don't buy them.
The longest I have left my birds unattended for has been 2 days, and I feel very uneasy even then.