Is it possible to retrieve past AIM Conversations?

First, the archive would have had to be turned on, This is a setting that is not default.
Second, that archive is stored on your local PC. If the PC is toast then no.
I am sure that AOL can retrieve it Server side with a subpoena.

If you saved them via AIM, your conversations would be found in your AOL email.

No, the conversations that you have on a Instant Messenger goes into a file that “archives” on your local PC, as @blueiiznh said.

If you want to start archiving the convos and have them accessible from wherever you are, you can download and use Dropbox.

And this is why I always tear down a toasted PC for parts. If you had the hard drive out of your old PC, you could do it yourself in a few minutes. Without that drive (or if the drive is toast), you have to go to AOL and you might need legal aid to get those released to you.

That is also why I use Pidgin or GTalk for IM; it logs by default ;)