You can download some of your Google data using Google Takeout. It’s far from complete, but if you’re still using Google services, it doesn’t hurt to download a backup once in a while.
The problem is that if your account is disabled, it's unlikely you'll be able to acces Gmail, IMAP or otherwise. I think Takeout has an exception so that it works even when your account does not.
It supports Gmail, Google Contacts, Google Calendar, Google Drive (formerly Docs), and Google Reader. By default, the app backs up your accounts every hour and maintains old point-in-time snapshots of your accounts for 90 days. All the data is available in standard file formats.
The Data Liberation Front lists which services can be backed up, and how to do it: http://www.dataliberation.org/