So just to make sure we're on the same page. You have a liner connected to your masonry chimney that goes all the way up to the roof? Does the liner go all the way to the top as well? So get us a pic of the connection from your stove into the chimney as best you can and maybe one of the best shot you can get of the chimney. The chimney is most likely taller than any other part of the house?
Turn off any of the following: Dryer, exhaust vent over cooking stove, whole house vent, bathroom vent(s). Close every window in the house and only open one window an inch or so, closest to the stove. You should be able to feel air coming in that window. If you need to open the window more, that is ok. Is the outside temperature below 50 degrees? Over 50 it's a bit harder to get a fire started.
With the stove out, light a match or a candle or use a lighter and put it inside the stove with the door open and see what happens to the smoke or flame.
EDIT: for clarity
That should give us enough info to help you get this figured out!