Haruhi (the Melencholy of...
)
Seriously, she doesn't look or act it particularly, but she is depressed enough to destroy the world on a subconscious whim!
Tsukasa (.Hack//SIGN)
If you haven't seen .Hack//SIGN, I recommend it, regardless of Tsukasa often being nearly as annoying as Shinji, the soundtracks are epic and the mysteries and other characters are quite engaging.
Fate Testarossa (MLGNanoha) near the end of the first season, just after her mother rejects her and reveals she is a copy.
Poor Fate.
Asuka Langley Soryuu (Neon Genesis Evangelion) near the end when she is in a coma from depression and getting hit by the crazy angel ray thingy and stuff
Seriously, you listed Shinji but not Asuka? Late series Asuka has Shinji's combined depression through the whole series beat!
Tomoe Hotaru (Sailor Moon) before being befriended
Seriously, her dad has gone nuts and mostly ignores her when she isn't possessed, her mother is dead from a tragic accident, the possessing spirit is messing her up, she's got healing powers her peers think she is some sort of monster for, no friends, has health problems that prevent her from doing anything even mildly strenuous, and basically is hugely lonely and likely has really low self esteem. (although she might lack the chi in order to do the attack, I think there might be potential for her to draw on her planetary energy to power it, depending on how you interpret the nature of the senshi and their powers)
"Health, Learning & Virtue will ensure your happiness; they will give you a quiet conscience, private esteem & public honor." Thomas Jefferson (1743 - 1826)