There are a few things that could have been going on here, and it's impossible really to know which.
First, yes, maybe you could have not been producing milk, but that is very very unusual. We know that there are some medical issues that can cause this (tubular breasts, PCOS maybe - but even then, these tend to produce less milk, not no milk). This is very rare, but slightly more common in people who have needed help to get pregnant, from what I know.
Second, as others have said, three days in, we wouldn't expect tons of milk. For some mothers, milk has come in at this point, for some it hasn't (depends on how the birth was, and how well, and often, your baby has been feeding.) For some mothers it often takes longer than three days to come in.
Third, pumping just isn't as effective as breastfeeding, as mombojombo has said. Plenty of mums breastfeed well for months, but never manage to get anything with a pump.
Fourth, there is a psychological element to let-down. If a mother is too tense (and who wouldn't be, after being told your child is dehydrated, and being poked and prodded), then sometimes let-down doesn't happen.
Did your breasts ever end up feeling full and sore?
A baby who is in serious danger at three days, from being underfed, is generally sleeping a lot - if a baby is not getting food at all, then they often sleep a lot to conserve energy. A jittery crying baby is generally not a starving baby, from what I know.