I have a Black and Decker Spacemaker type coffee maker. The water reservoir is detachable for ....

When the water holding container is removed, check under the container. Usually and most likely a water stop plunger or plug that closes to prevent water from spilling out. That device may be stuck closed.
Also check the location where the container fits. Where the water drain place meets the water holding container. May have a valve stuck closed, something like a baffle or anything which may be in the water line, etc.

Keep in mind that the quality of the product is unusually poor. The problem is that the component that holds the filter and coffee does not fully seated, which prevents the plunger from working properly

The two holes on the top of the back are supposed to engage two dimples when you slide in the component. They do nto becaues the holes are too big, the material used is too thin, and/or the holes are out of alignment.

I solved this problem by forcing mollies like the kind you would use to attach a screw to drywall into the holes. They have to be the right size. This effectively made the holes smaller and reinforced them. The component will now seat, which will allow the plunger that opens the hole to the coffee pot to work properly.