Bought a 60s house with a basement
The ground floor is finally renovated
The basement (garage, laundry room, storage) shows moisture in the walls.
Drainage will occur in week 3 of 2016 so I can't fix the walls until March.
Non-insulated slab.
Question: can I start with the floor and lay tiles before it is drained?
Well, you should be able to do that, the slab won't get much dryer just because you drain it, the moisture comes from the ground beneath the slab. As long as you're not going to waterproof, it doesn't matter how wet the slab is.