Google's translation isn't off too much.
却 is an adverb which is used more or less like "yet", "however" or "and yet" in English. I say "and yet" because I often see it used as a conjunction, in place of 反而.
这句话那么简单，却点燃了我 (= this sentence is so simple, and yet it set me on fire)
万千 means "a myriad", also in English used figuratively to elegantly express a large quantity.
感慨 means something like "full of sorrow". Mdgb says "rueful". Zdic defines it as 心生感触而发出慨叹. Which essentially is a feeling of such sorrow that you can't withhold sighs and moans. Also, given the proposed synonyms (感叹, 慨叹) it seems it's used in a verbal position. It's seems used like a stative verb.
So if you put it all together:
我 (I) 却 (however, yet) 为你 (for you) 万千 (myriad) 感慨 (rueful, feeling sorrowful)
It roughly means the subject's feelings are many and nuanced, but all of them related to sorrow and sadness.
A fluent translation (somewhat poetical) might be something like:
And yet for you I let out a multitude of sighs
or, taking 万千 less literarily, so many feelings that the subject is overwhelmed.
And yet for you I'm overwhelmed by sorrow