No Linux expert am I. I know nothing of Fedora either. I do know something about dialup modems and using them in Linux. I’m not sure what you mean when you say you’re using a USB card.
I searched but couldn’t find your modem. I did find this:
http://www.anydata.com/modems.php
Is your modem similar to one if those? Is your modem external. Does it plug into a USB port?
USR makes an external dialup USB modem model 5637. Here’s what I read in the PDF users guide under troubleshooting:
Linux 2.4.20 or higher:
A. Verify you have a USB modem driver (CDC ACM) compiled into a Linux kernel 2.4.20 or higher or as a loadable module for your kernel.
B. Verify the PWR LED on the modem is lit.
C. Unplug the USB modem from your computer, then plug the modem back in. If the PWR LED does not light, try another USB port on your computer.
D. For advanced troubleshooting information, see the Linux folder on the USRobotics Installation CD-ROM
Another thought: IIRC I once had trouble finding the right verification method for my ISP. I tried them all until I found the right one. IIRC I settled on PAP. Before I found the right method the modem would try to connect and then just die shortly after making a connection.
I hope my ramblings helped you a little. Good Luck.