歌詞： 「傘が無い」 (lyrics: "Kasa ga nai")

井上陽水の歌です。 / Song by Yousui INOUE.

都会では自殺する若者が増えている
toukai de ha jisatsu suru wakamono ga fueteiru
in the city, more and more young people are killing themselves

今朝来た新聞の片隅に書いていた
kesa kita shinbun no katasumi ni kaiteita
it was written in a corner of today's paper

だけども問題は今日の雨　傘がない
dakedo mo mondai ha kyou no ame kasa ga nai
still, for that problem, for today's rain, i have no umbrella
[I missed the contrast here. "But the problem is today's rain" would be better.]

行かなくちゃ　君に逢いに行かなくちゃ
ikanakucha, kimi ni ai ni ikanakucha
i have to see you

君の町に行かなくちゃ　雨にぬれ
kimi no machi ni ikanakucha ame ni nure
i have to go to where you live, even if i'm soaked in the rain

冷たい雨が　僕の目の中に降る 今日は心にしみる
tsumetai ame ga kyou ha kokoro ni shimiru
today the cold rain soaks straight through to my heart

君の事以外は　何も見えなくなる 考えられなくなる
kimi no koto igai ha kangaerarenakunaru
i can no longer think of anything but you

それはいい事だろ？
sore ha ii koto darou
and that's probably a good thing /
（ironically） awesome.
[with no punctuation, that だろう is hard to parse.]

テレビでは我が国の将来の問題を 誰かが深刻な顔をしてしゃべってる
terebi de wagakuni no shourai no mondai o
dareka ga shinkoku na kao o shite shabette(i)ru
on TV, someone is talking with a serious face
about our country's future

だけども問題は今日の雨　傘がない
dakedomo mondai ha kyou no ame kasa ga nai
but, still, the problem is this rain. i have no umbrella.

行かなくちゃ　君に逢いに行かなくちゃ
ikanakucha kimi ni ai ni ikanakucha
i have to, have to see you

君の家に行かなくちゃ　雨にぬれ
kimi no uchi ni ikanakucha ame ni nure
i have to go to your house, soaked in the rain,

冷たい雨が僕の目の中に降る
tsumetai ame ga boku no me no naka ni furu
the cold rain falling in my eyes

君の事以外は何も見えなくなる
kimi no koto igai ha nanimo mienakunaru
i can no longer see see anything but you.

行かなくちゃ。。。など

The excellent blog Foreign Language Music has some really helpful grammatical notes. Among: turns out 心に染みる carries a connotation of stinging, not just soaking.