I have an Avenir floor pump that I've been using with my presta valve-equipped bikes for probably over 10 years now. It's got a Silca head on it with a brand new seal. Earlier today I successfully inflated a road tire, the proceeded to attempt inflation the tires on a cruiser for my wife (it has presta valves too) to no avail. I then tried pumping up the tires on three different bikes, but no dice. I'd put it on a tire and pump, and the pressure gauge would go up then go back down. If I let go of the handle, it'd shoot up to a higher position like the pump was holding pressure but none was going into the tire. I could not hear any leaks from the pump. When I put my thumb over the hole on the head and pumped, I could feel air coming through. At first I thought this was just due to old presta valves on some of my tires, but I moved around to different bikes and newer valves and had the same problem. And yes, I did loosen/push down on each presta valve before attempting inflation. Is my pump hosed? The behavior strikes me as kind of odd.
When I had this issue I thought my pump was busted. Then down towards the base of the pump I noticed a knob so I tightened it. Problem solved. I don't know what that knob is really for, maybe to oil the pump or something, but when it was loose all the air escaped through it. Check down at the base for something like that and make sure it is finger tight.
That's what I think too. I'd "burp" the little stem on the presta valve. That usually solves the problem you describe.
I burp the stems every time, and mentioned that in my original description. Still no dice. I agree that it seems like the pump is compressing the air, yet it does come out the end of the pump head when it's not attached to the valve. Weird.