Yeah...doesn't sound right at all. The motor doesn't 'blow' it 'sucks', meaning that the water free-flows into the intake and the impeller forces it back through the out tube. It sounds to me like some part has broken free and is actually stopping the water from flowing past a certain point near the inflow of the head unit. Since the pump-start feature wasn't working, my guess would be that what you are seeing is related to that part not working.
Say for instance that the pump button, when you push it down, forces a spring-loaded bladder of some type down, and then when you let go it creates a vacuum to 'suck' the water into the inlet tube - or it could create the vacuum when you push it in, either way...let's say that whatever is supposed to move one way and then back is 'stuck' in one spot. This would cause the water to stop at that spot.
The fact that you can blow air through it mean that it must be something that, when the water gets to it, seals the passage due to the pressure, like a backflow preventer.
Wait...this may sound stupid, but do you have in/out reversed somehow? You have to suck on the outlet, if you suck on the inlet, you would get water to the head and then it would hit the backflow preventer (assuming there is one).
Still I'm guessing that something is wrong in the head unit. I think you can remove that assembly and you should be able to see the primer plunger assembly, the channel for routing the intake water, the impeller, everything. I remember because I took one out of the box to check it out.