Yes, everything MM said.
It was not clear to me how you were accessing your e-mail ... whether or not you had at some point installed the AOL Browser/Desktop 9.x
If yes, then you will have an Organize folder containing your Personal Filing Cabinet (a Profile by any other name).
{XP example: ...\Documents and Settings\...\Application Data\AOL\...\organize}
I have already detailed above how to download all selected e-mails to your Personal Filing Cabinet (in the Organize folder).
In the Organize folder there are (I think) half a dozen files called your_screen_name with varying file extensions (1.AUT,abi,aby,ARL,BAG). The file with no extension, called simply your_screen_name, is the one containing the meat. You can double-click on it and open it with (for example) Wordpad. It's all there, albeit a bloody mess, and you can pinpoint particular e-mails fairly quickly as long as you know what it is you're looking for (use Search). [Annoyingly, the Windows search function doesn't find specific text within Organize folder files.]
You can save the entire Organize folder to your backup medium of choice. You could also copy PFCViewer (already linked to) to the same backup drive and use it to, um, view your PFC.
If you do have some variant of the AOL Desktop installed then you have nothing to lose by trying it (except precious time).
However, I wouldn't advise anyone to install AOL Desktop for the first time unless they were able to image their drive first ... it's probably not as pernicious as it used to be but it's still going to eat at least 100 megabytes of storage on your system drive. If you're feeling under par it's perhaps too much of a fag ... and certainly too risky.
That said, I've experienced no problems:
AOL Desktop 9.6
As an aside, we've long been quite happy using Pegasus Mail program on Windows but (according to Wiki) development ended recently.