Which model?
Test the draw of your chimney by lighting a bit of newspaper and dropping into the hole where the hotplate sat. if the smoke is pulled towards the flue, you’re OK there. Get it swept anyway.
Look down from the top towards the burners, from what you describe, I suspect you’ll find a great clod of oily soot dislodged by the wind is killing the draw above the burners around the boiler pipes.
remove the burners and completely de-soot and de-coke, removing and discarding the wicks.
Brush and vacuum out the whole thing until like new.
Put back together and light, after leveling the burners of course.