Gmail – After revoking 2-step Gmail verification can’t access account on apps, only at gmail.com

I tried the 2-step verification for Gmail a few days ago and created app-specific passwords for my mail clients (Apple Mail, Sparrow, iPhone, iPad) and they all worked out fine.

Last night, I tried logging on Gmail.com on browser on my mom's computer. Naturally, with 2-step on, it would send me a code to verify my account via SMS. Waited half hour, still no SMS. So I tried the calling option, got a call, but no sound on the other end so I still didn't get the code. And I didn't save the backup codes (didn't realize there were such a thing) so I freaked out and reset everything using their 2-step troubleshoot form.

This morning, I got an email:

Good news — you’re just steps away from regaining access to your account! To reset your password and sign in, follow these steps:

So I did. Changed my password, recovery email address, secret questions and the like.

And I went in to the 2-step settings page to turn it off as it's so troublesome. Revoked all my individually created passwords for my apps, and went in to change the passwords to the main Gmail passwords on all these apps.

And lo and behold: "Password incorrect".

I thought I entered the password wrong. Tried logging out of Gmail through a browser, logged back in, but no, still incorrect.

I tried logging back in on iPhone Mail, Apple Mail and Sparrow. "Password incorrect". Didn't have to try my iPad to know what it would say.

I can now only access Gmail on gmail.com, not any of the apps.

Gmail is my main email address and I would like to access it from more than just the website through a browser.

How can I get access to Gmail through other apps again?