Icedove Mail

So one account works, but the other doesn't.
Did the same account work on Icedove before but only recently stopped working? If it did work before, what changed?
Did you make sure that you entered the correct user name? (some server software and setups require your log-in user name to be your full e-mail address and I'm not sure how Gmail does it)
Is your password correct? When in doubt, delete your saved passwords for that account in preferences -> security -> passwords -> saved passwords and try again.

Are both accounts in Icedove using the same settings to access the server? I mean the imap port and security method in the "server settings" of your account settings, and the smtp port and security setting in "outgoing server (SMTP)". According to their site, Gmail only supports IMAP port 993 and SSL/TLS as security. For the "outgoing server (SMTP)" settings, you can use port 587 for STARTTLS or 465 for SSL/TLS. Trying to use STARTTLS for IMAP on Gmail may fail for example.

What does the error message in Icedove say, exactly? Icedove's error message were not very helpful in my experience, but seeing the complete error message can't hurt either.

Maybe Gmail even blocked your external access on that account for doing something they didn't like, like sending or receiving too much data.