(I was unsure of the fourth and fifth character).

I'm fairly certain that I read it correctly, except for the fifth character.
The fifth character in the text looked very similar to that but it looked like
there was a bottom (almost-) horizontal stroke going from left to right, but I
couldn't find a character more similar to it.

I think it means something like: Valentine's day is always depressing, but
this one should be the most exciting day

or the opposite:  
It's the first Valentine's day that is depressing, and it's supposed to be an
exciting day
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question
translation
What does this mean? Friend gave this on a piece of paper, and wanted me to translate this: こんな憂鬱なバレンタインは初めてやワクワクイべントのはずなのに!
> こんな憂鬱なバレンタインは初めてやワクワクイべントのはずなのに!

your translation : " _Valentine's day is **always** depressing, but this one
should be the most exciting day._ ".

I think it's almost there, however, I am not sure about from where " _always_
" comes. It contradicts to 「初めてや」: "for the first time". So, you don't need it
and add "for the first time" into your sentence (Probably I will add "this" in
the beginning of the sentence).

Your 2nd translation : " _It's the first Valentine's day that is depressing,
and it's supposed to be an exciting day._ " is almost perfect to me. Probably
you can add "so" or some emphasis before depressing.

* * *

For the kanji part, it was also challenging for me remembering how to read and
write「鬱{うつ}」for the first time. From my personal experience, I broke them down
into the familiar components into「木」,「缶」,「木」,「凶」and「ウヒャー」since its strokes
were so intricate for me. Then, I tried to connote them as yucky things and
practiced how to write them over and over again.

I remember the member from "L'Arc-en-ciel", one of the most famous J-Rock
band, had needed to remember how to write their song title
:[『夏{なつ}の憂鬱{ゆううつ}』](https://www.youtube.com/watch?v=iIDwidnRp-Y). You can read
kanji, but you can't write it sometimes, so don't worry about that too much.
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answer