You should be cleaning your stove and pipes out at least once at the end of each heating season. If you're burning a lot of coal, mid season cleaning is needed. If you are using a power venter I believe the recommendation is to clean it and the flue pipes out (or at least check them for build up) after every ton of coal burned (and at the end of the season). This is crucial for both maintaining proper draft and for protecting your equipment from corrosion during the off-season.
Fly ash will build up in the pipes, the venting tunnels of the stove, and the blower of a power vent unit, causing the strength of the draft (be it via motorized vent or natural chimney draft) to diminish over time. Adjusting the barometric damper will not fix the problem, at best it will only mask the problem for a short period of time.
Also, make sure you have at least one working carbon monoxide detector installed. This safety device is a must for any coal stove installation (or really any heating appliance), however with poor draft comes increased risk for CO infiltration into the house.
EDIT: You posted while I was typing.
You are right to shut it down and check things out. It is good you had the CO detector installed. With your LL stove there should have been a manual and a DVD supplied which detail the cleaning and maintenance of the stove (and the power vent unit, if you're using one). If in doubt call your stove dealer for help or references to local chimney sweeps that can help you out.