Well actually, I've seen some textbooks for non-native learners so far since I've been giving responses for over 9 years even only in this forum. ~ていく/くる has another meaning, as explained in the site you linked, and it's taught in beginner level (Genki Ⅱ, if my memory is correct). I don't think it's wrong to judge that a textbook that doesn't explain the modifying clause or ~ていく/くる at all is not decent even for beginner's level.
Honestly, we've been seeing many learners who tried to translate lyrics without knowing basic grammar. I remember a member of this forum. She said she didn't learn Japanese properly, but had been translating Japanese song lyrics for over 10 years. She contracted for a job to translate a company's home page into Japanese, and asked us to proofread it. Her translation was... totally gibberish. It didn't make sense at all, literally at all. A member pointed out that to get paid for those kind of work was a fraud. Few years later, she asked about a lyrics she was translating at that time. She interpreted a modifying verb as the predicative even in that time, just like you did for けむる. This is exactly the reason why Mike-san wrote "Naturally, the thread will end up being us doing the translating for you." in this thread.
Again and again, my points are; song lyrics are not appropriate as a learning material, you need to get a decent textbook and learn from it, and nevertheless if you seriously want to learn something through translating this lyrics, you shouldn't leave 凍えたまま just as "frozen". There is no problem with asking about ~ていく/くる. We would be able to explain it just like in
this thread or
this one, but your reading comprehension of Japanese will not improve at least efficiently and/or effectively without using decent textbooks, I believe.
Verb + ていった ( = teitta) From the past until the time when speaker is thinking.
Verb + てきた ( = tekita) From the past until the time when speaker is thinking.
Sorry for nitpicking, but are those two expressions the same in meaning?
道路わきのビラ - villa(s) of the sideroads
と - and
壊れた常夜燈 - broken nightlights.
What am I doing wrong? This is one of those sentences which look really easy... it there more to it?
I don't know what kind of dictionary you are using, but is "villa" only the meaning of ビラ in your dictionary?