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.
Not enough information.
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.
Your account still exists:
I don't know how to see your pixiv ID since you haven't uploaded anything.