"no modem detected or
unable to establish a connection with aol service"
This sounds like the modem is either incorrectly/incompletely installed and/or she can't for some reason authenticate to AOL (check the access numbers, username, password, call them to verify she's an active user).
I don't know if you can logon to AOL with a generic dial-up connection, but she could give this a try:
Go to Start > Programs > Accessories > Communications > New Connection Wizard
Choose "Connect to the Internet"
Choose "Set up manually..."
Choose "cOnnect using dial-up modem..."
Enter "AOL" as the ISP name
Enter the access number (she should have a few of those, pick one for now)
Enter the full username (ex.
U2Kitten@aol.com)
Enter the password
Check only the top option
In the last window, check "Add a shortcut..."
Now there will be a new dial-up connection on the desktop. Click on that and see if it can dial in and connect. Since it's not using the AOL software, if it connects, she can open IE or whatever internet browser she's got.