AOL launched around 1991 if I recall. I remember watching with great interest (I think I may have been in some kind of beta program) as it was obvious (at least to me at the time) that digital communications with a graphical UI was the future. (At the time in the US, there were a few commercial information services that were textual, General Electric Network Information Exchange and CompuServe were the big ones... followed by Prodigy which basically looked like teletext or a Bloomberg terminal for the home- it was clear that something better could be done, which ended up being AOL).
The original AOL client shipped for DOS with Digital Research's GEM widget kit, it wouldn't surprise me if they used additional DR hardware and software on the backend (VAX anyone?). When I worked on the AOL project, I would see e-mails from AOL ops (from AOL screen names, no less!) about how they would take scary and unique sounding things like "access rotors" down, so I suspect that given how early the launch was, the backend was extremely bespoke simply because they were making things up as they went along in order to launch a new and unique thing.
It wouldn't surprise me one bit to learn that it ran on VAX, HP3000, AS/400 or perhaps something even older and larger. You didn't hear about horizontal scaling nearly as much back then, most scaling consisted of "buy a bigger computer."