The first thing I would do is take back the water distiller. their is no reason to spend that much money. Maybe your distiller is used? Some distillers have to be cleansed out good or the don't work. citric acid works great. My kenmore distiller (discontinued) can be filthy and still make clean enough water. All you need is a small one.
The silver puppy will automatically turn off when you reach 15 or so PPM. If your water is already 10 ppm of mineral contamination deposits the silver puppy will turn off early.
My silver puppy works great and I haven't seen any that I like better. I'm sure they will send you another unit if you suspect something is wrong. It's a big coincidence that you have 2 different sources of distilled water and it still isn't working.