I do not think it is possible not to have any diving response at all. It may be stronger or weaker; faster or longer to kick in; individual effects may occur with variable intensity; but I do not think it is possible that the body does not react at all.
The question in such case is rather why the diving response at such individual does not occur with expected force. There are external factors (i.e. water temperature), individual predisposition or experience/training (studies show higher diving response at regular freedivers, though it might be also the consequence of natural selection), and physiological aspects having impact on the DR. And one of the most important factors is the CO2 level, and consequent blood pH. So of course, the more you hyperventilate, the lower chance for an early and deep DR. And the lower DR, the less the DR will compensate the negative effects of hyperventilation.
One could tell, if there is no diving response, hence no trade-off between hyperventilation and the DR, then deep hyperventilation would be the best way. However, I believe it is wrong anyway - first, as I wrote, there is always some DR (even if quite weak), and second, some of the negative effects of hyperventilation are so significant that they impact the maximal performance anyway. Most importantly it is probably the decreased hypoxemia tolerance, which then leads to a premature blackout.
When comparing maximal attempts with and without hyperventilation, we have to differ between physiological and psychological maximum. Physiologically taken, as explained earlier in this thread, the theoretical maximum is a trade-off between the advantages and disadvantages of hyperventilation, and also its influence on the DR. But the real performance is more often interrupted because of the psychological barrier, especially if done under high CO2, hence you then do not really compare the maximal physiologically possible times.
Perhaps, in your case, the weak DR is influenced by subconscious hyperventilation even when you think you do not hyperventilate at all. But of course, there may be also other physiological conditions suppressing the DR. Perhaps frequent training in conditions improving the DR (cold water, no thermal protection on extremities, no mask, high CO2, stress, ...) may help waking it up better, and perhaps it will then kick in easier in more comfortable conditions too. Also frequent deep diving may help training the DR - the fact that until recently you only knew the pool and did not dive in open water, may be a reason for the weak DR.