I got a new laptop and found A) I couldn't log into Pixiv and B) when I try to request a reminder/new password I keep on getting a "user does not exist" sort of error.
I tried clearing cookies, I tried clearing cache, and i even tried going into IE but no luck.
Does it work on your old laptop/PC? What login information did you use? Did you forget your pixiv ID / email? What's your ID? Are you even on http://www.pixiv.net/? Did you provide the correct e-mail address at http://www.pixiv.net/reminder.php ?
Most likely, you tried to log in using your nickname and it didn't work. Use your pixiv ID or the e-mail you provided when signing up.