Exchange "Password incorrect" lockout of iPhone

Question

iPhone 3GS
iOS Version 5.0.1
Build 9A405
I have an Exchange email account set up on my iPhone. Now when I turn on my iPhone and "slide to unlock" I am presented with a popup window saying
Password Incorrect
Enter the password for the
Exchange account "Exchange"
{Password   }
[Cancel] [OK]
Entering the formerly correct password then [OK] does not satisfy this challenge, the popup returns. If I attempt to [Cancel] the popup returns. I cannot get past this popup window. I'm locked out of my iPhone.
I no longer have an Exchange account. There is no current password to any Exchange account.
I need to gain access to my iPhone in order to remove this account from the email settings. I am unable to get beyond the above popup to do so.

Answer 1

I also just resolved the problem, but differently, and the issue was on the GMAIL side. This is a variation on some people's advice to allow App log-ins.
If you sign in on a computer browser and look at the top of your Gmail mail window, you may see a line above the message list that says something to the effect of "Unusual sign-in location: There have been multiple attempted log-ins from a suspicious source." My first two were from when I was traveling.
I confirmed that those locations were legit, and then there was another prompt asking about another suspicious repeated attempt sign-in, which was my iPhone Exchange, although it was not labeled as such. It gave me an option to forever accept sign-ins from this application (Exchange). I accepted, and all was fixed!
Hope that helps some people.