When you say 'new' mortar, do you mean new from the store or a new batch of the same 'old' mortar. Old mortar should never be used except as landfill.
Assuming you mean you bought new mortar...
Is the mortar adhesive hard even though it's still wet? If so, you're using a non-latex modified type mortar. If the tiles are not sticking you are probably mixing it too dry. I generally mix mortar type adhesive so it's just thick enough to stand up when spread with a notched trowel.
If the mortar you're using is latex modified, either by adding liquid latex or if the latex is already added to the mortar, it must be able to dry. Latex modified mortar does not set like regular mortar. Apparently the concrete is sealed or otherwise not porous enough to allow for drying.
Finally, how soon are you applying the grout. I generally let mortar adhesive dry for a couple of days before grouting. On a cold floor I might give it a lot longer, maybe 3 or 4 days.
Also, can I safely assume nobody is walking on it before it's fully setup? Sorry, but I have to ask.