BleepingComputer.com: Suddenly my iPhone can't get my email from Gmail?

I have an older iPhone - iPhone 2 (I know, I know... but it works and I like it) and I've had my Gmail account connected since day 1. Never had problems. Until today. Suddenly, I'm getting a pop up message that the username and password do not match. I did not change my password, and haven't changed it in a while. My first thought was that my account got hacked, but I was able to log in via Firefox with no problem. I then tried to log into Gmail from the iPhone via Safari - and had no problem. I deleted the account into from the iPhone and re-added it, but it won't let me access the emails. I rebooted the iPhone, did nothing (not sure why I did that, but I did). I even went so far as to change the password on my Gmail account via my home PC, and then delete the account from my iPhone, and then re-boot the iPhone and re-add the account with the new password - still getting a message that the password is incorrect.

Any idea why this is happening to me? I've been relying on this iPhone to get emails throughout the day for years and I don't think I can live without this feature...