My cuisinart base was fully frozen, the custard was chilled properly, what is going on!?
Is the lid properly engaged? If the dasher is up just a smidge more than it should be (needs to rest in that little dimple in the bottom of the freezer container) the lid won't catch on the base and the dasher can't do its job. I had that happen once. Very frustrating.
Did you put any alcohol in the ice cream?
Both answers make sense ... But I wonder if you actually cooked the custard correctly? As a chef of 35 years, I still to this day dread over-cooking custards. Was it runny, or beginning to thicken when you froze it? Did you chill it prior to placing it in your freezer?