unconscious, oxygen-starved and frozen-stiff in an unpressurised environment at cruise altitude of 34,000ft?
I would take issue with the assumptions here. A depressurised cabin is not necessarily cold unless the air-supplies are inoperative and/or there is a big hole where a window used to be. We know that following a packs-off take off the air supplies were restored so warm conditioned air would have been supplied throughout as the system attempted to bring the cabin to the demanded temperature.
With the outflow valve left in [MANUAL] for the entire flight the pressurisation would have progressed abnormally leading eventually to a hypoxic environment as they climbed. As the engineers had carried out static pressurisation tests on the ground pre-flight, The probability is
that the valve was left in a near-closed position.
If you take off in an aircraft that is totally failing to pressurise then it is pretty evident - your are obiged to clear your ears frequently as the cabin ROC is 2500fpm as opposed to about 500fpm. In short - it is a cue difficult to miss... so how come...? The probability that the outflow valve was static in a near-closed position would allow some pressurisation but the situation might not be recognised as so abnormal as to give rise to concern.
In this configuration the resulting cabin altitude when at FL340 will be a matter of pot luck. If the cabin ends up (say) in the high 20,000's you will have an adequate amount of oxygen to sustain life but insufficient to sustain consciousness in the majority of subjects.
The cabin oxygen PSU's drop at 14000'. The chemical oxygen generators in the are designed to function for a minimum of 12 minutes. They don't stop after 12 minutes but the level of oxygen produced tails off until the production ceases altogether much later. If you pass unconscious with the mask still on your face you will be getting SOME oxygen for some time thereafter. As for the 8yo child surviving after the crash - we already know that children have survived for extraordinary periods in water under ice so perhaps children are better equipped to survive hypoxia that adults?