今週は、訳あって、憂鬱な一週間になりそうだ。

、、。

For reasons I won't go into, this week looks like it's going to be a gloomy one.

Literal

This-week [topic-は], reason exists-[and-て], melancholy-[attributive-な] one-week [to-に] seems-to-become-[seems-そうだ].

訳あって ('for reasons, with a certain reason') is a fixed phrase implying the speaker doesn't want to specify the reasons. Uses the noun 訳 ('reason, explanation') + あって (te-form of ある, 'there being'). 憂鬱 ('melancholy, depression, gloom') is a tricky kanji pair known for being one of the hardest kanji combinations to write. ~そうだ here is the appearance evidential ('seems like').