Mail isn't going to do it for you then.
With the exception of the Trash, Sent, and other standard folders Mail can't create local folders. With an IMAP or Exchange account you can keep the folders stored on the server, and sync. My recommendation in that case would have been to copy the folders to the server. You could still create a second account, perhaps a GMail account or the @icloud.com account, and copy your folders to them. At that point you could save stuff across accounts to the GMail account on both iPad and computer.
If you get a new account you could just use the online folders, or slowly transfer your traffic to the newer account. Google has the option to access an import POP accounts, to make sure you don't miss emails from those that don't have your new address.
Double check with Earthlink and see if they have an IMAP account options. It would be even easier to change your account setups and transfer your local folders to the server. Last I heard, they did not, but that was a couple years ago. They might have moved forward. It could happen.
Another possibility, if all you need is read only access, is to export the folders in Thunderbird. Depending on the export format you may be able to find a reader app in the App Store. I know there are one or two for the standard Outlook export format (but only one or two).
Finally you could get a third party email client for the iPad. There are a few that handle POP accounts and will create local folders. I have no idea if how you can transfer your current folders to the iPad. I don't really recommend this, but if local folders are an absolute must, third party apps are your only choice for now. ibisMail is the only one that pops to mind at the moment. I haven't looked into it for a long time, so do your own research on this subject.
Good luck.