Is とうとうりん here meaning finally? And what about りん?
とうとう is "finally".
There is an uncommon adverbial phrase りんと (凛と in kanji), which usually means something like "in a cool/gallant/dignified/cold manner". See this entry. But this meaning does not make much sense to me in this case because the word is used to describe an inanimate object. I believe this is something heavily dialectal, or an idiosyncratic/creative expression of the author. Meaning-wise, it should be the same as まったく動かない or ぴたりと動かない.