My new mountain bike tyres with presta valves do NOT inflate
Some Presta valves can accept stem extensions and the upper valve body (containing the little nut you unwind to add air) can be unthread from the lower part to accept extension. Anyway, this sometimes comes unthreaded with the use of a presta  to Schrader adapter and air is lost. Perhaps this is loose and air isn't getting into tire/tube but escaping here. There are tiny wrench flats on the upper valve body of many Presta stems. If present in your case, try snugging it up.
Another problem might be at the pump. Some hand pumps require a lever in the correct position to deliver air into the valve. Make sure you fully engage the valve and if the pump has a lever try both open and closed positions (here I mean lever up and lever down positions).  Hand pumps that can switch from Schrader to Presta set-ups utilize the lever in opposite positions for filling depending on which system you're doing.  The limited # of ones I've seen, the lever is placed "up" or 90 degrees to the pump body when in Presta mode. So with the lever down (parallel to pump body), you fully engage the open Presta valve and then lift the lever to the 90 degree position and begin pumping. 
A presta tube can be partially inflated with your mouth, should you choose, by pushing the unwound valve tip with your tongue whist you blow into it. You can check the valve integrity this way. I recommend a cold beer with that dish. 
My guess is your pump end is not engaged correctly or is faulty.