Time Warner Cable - Cable Phone & AOL dialup

I have been unable to find a definitive answer to this simple question. Friend ("client") has TWC Cable for TV and had AOL Dialup for Internet, and Verizon (landlines) for phone. Switched Verizon to TWC Cable phone. Will AOL Dialup still work if called over TWC Cable Phone connection? Unfortunately I cannot easily test this as the PC used is kaput - and gone. Friend does not want to spend $ on Cable Internet - "likes AOL". Can replacement PC use Dialup modem to call AOL? TWC phone Tech Support says it will not work. Also says some FAX machines will not work with TWC Cable Phone,. TWC Tech who did install of Cable Phone connection would have checked the PC modem connection (maybe?) - except there was no PC to check it with. Or is a Cable Internet card needed, and AOL Dialup no good - "must" switch to TWC Internet? (I don't understand how TWC can sell phone connection that will not work with some FAX machines) - Brian