I always look at the AOLTimeWarner merger as the thing that broke them, distracting them at the moment they should've been prepping to roll out broadband. I also look at that merger through the lens of "don't fight a land war in Asia" in terms of breaking empires -- "don't let your company acquire Warner Bros.".
AOL did exactly the right thing. They knew their stock was overvalued and did some shady accounting to prop their stock up until the acquisition and it immediately crashed.
How could they “get into broadband”? They weren’t going to be able to create the last mile infrastructure. We see how that worked out for Google.
https://arstechnica.com/information-technology/2019/02/googl...
They couldn't buy the last mile, but they could have gone for an infrastructure play. You buy your broadband from the local phone or cable company, and they give you an AOL email account, the default portal is aol.com, they nudge you towards the all-in-one AOL client, etc. The local cable companies don't have to figure out anything but being a dumb pipe, and they can get a revenue stream less coupled to selling overpriced dialup. (They did have a "bring your own connection" plan at some point, but it was probably an easier sell to include it as part of a $75/month DSL/cable subscription rather than as an independent line item.
Maybe use their temporary dial-up riches to line up long-term rights to premium content. I suspect before YouTube took off, nobody knew the potential for online video, and they could have probably locked in contracts at very low prices.
Time Warner Cable (now Spectrum) was literally one of the pioneers of cable broadband. It seems like the best way for AOL to “get into broadband” at the time might have been buying Time Warner.