Dial-up was fine back in the days of text-based online systems and simple graphics, but once video, high-res animation, etc became common on the Web, people needed much faster speeds to get online and broadband and other fiber-optic systems basically answered that demand. By 2001 or so, dial up modems were loosing to ethernat, cable and DSL modems-the graphics and memory of web sites, browsers and everything else was increasing greatly and slow dial up just couldn't handle all that.
I think the thing that really killed AOL (and those old-school type chat rooms) was not only AOL's sale to Time Warner circa 2000, but also a vast increase in competition and changing technology, that AOL simply did not adapt to, or did not fast enough. Had broadband from 2002 on, so it became a pain to also have a dial-up for AOL.
I started using AOL in early 1994, before it really took off and I stopped using it sometime around 2003, though even by then I had been using it less and less in place of other things like Yahoo and such. I seem to recall AOL allowed up to five separate screen names on an account.