Does seem strange. Given you managed to deflate the tyres with a Schrader the valve cannot be stuck closed which sometimes happens if it hasn't been used for a while. The Schrader has a little pin in its centre to open the valve when you are pumping things up which will be why it deflated the Presta. The Presta should be clear so that the valve closes under internal pressure. I might only guess that something in your pump fitting is holding the valve open. Since you mention something like a dual headed pump I assume it has the rubber sleeved head. Check that it hasn't suffered any internal damage and make sure it is properly mated to the valve stem, spit helps.