ealtman When you say you can't edit the settings or set it up from scratch, is that because you're not an admin on the system or there's a problem with a forgotten password? If the latter, you can reset an admin password as long as you have access to the database - see the post from ntozier here https://forum.osticket.com/d/5450-admin-password-reset/2 (it's an old post, but as far as I'm aware should still work - backup your database beforehand though just in case!)
Once into the admin settings, you can check and verify the settings - you should also receive a bit more detail about any authentication errors when you update the settings (such as finding IMAP isn't using SSL when it should, or similar).
And I know you already know this, but it really is worth upgrading to a supported version - you're only one version behind one of the current supported ones (1.14.x... 1.13.x was skipped due to Americans and their phobia of 13 😉 ) although note that you'd have to upgrade PHP too.