I think the problem, Linnet, is that the AOL software may have a default setting of using a dial-up modem, hence the error message.
Even with a USB-based ADSL modem, the 'Network Connections' panel will normally show some 'dial up' connection.
I'm using a USB dongle from "3" (mobile network Three) and even that has a network object describing itself as a dial-up modem, with a phone number of "99**1#" {strange but true}
Back to your PC and why it works with MS Internet Explorer...
If you use the Control Panel and view "Internet Options" then it probably says "Never dial a connection" under the "Connections" tab. That's the default for all internet software. However, AOL doesn't care about that setting, and still tries to use the dial-up modem it thinks is installed.
The thing about Microsoft is they tie their software together, but other firms (competitors) sometimes ignore the Microsoft settings.
For example, in MS Outlook Express (e-mail) or MS IE (browser) the "File" menu has an option to "Work Offline" (so it would prevent the software from dialling a modem, if one was using it, to let you prepare an e-mail without costing money by making a chargeable call.
If you set 'work offline' in either Outlook or Explorer, it will affect the other software too. However, you can still have a connection (eg through your Netgear router) and Firefox or Opera browsers don't care that Microsoft software thinks there's no internet connection, so they will still work! AOL trying to use the dial-up modem is part of this same situation, ignoring some settings in the control panel.