Sticky / broken floor pump head?
Most likely a gasket/o-ring blew or some debris is caught up in the internals. I wouldn't use WD-40 as the light kerosene can deteriorate o-rings or some plastics. I'd try with some canned air / compressed air. 

If your pump head is well designed, you can take it apart and rub some silicone lube on the o-rings and mating surfaces to help restore the seal. If you don't have silicone lube, look for a grease that is o-ring/plastic friendly (WD-40 and vaseline are NOT o-ring friendly). In the image below (of a portable not stand pump) the o-rings and gaskets/plunger are the two circled objects in the very middle. 



Note 1:You have to BE VERY CAREFUL of both the order and direction of parts in a pump head, flip them around and the pump head won't work or will work poorly. Taking photos of the pump head while you take it apart is highly recommended.

Note 2: Your pump will be more complex because it's dual-head and designed for one side (presta/schrader) to be automatically closed when the other side (schrader/presta) is in use. 

If this doesn't work, it might be easier / faster / cheaper to just replace it. Do a search on amazon (or your LBS) for "replacement bicycle pump head" or "bicycle pump head upgrade."