The modem tested fine and dialed up at my vendor's analog line. But I could not get it to dial at all at my home phone analog lines. Either of my two analog phone lines works fine with the phones and with my two other computers existing computer equipped with an analog modem. (One of these computers is an HP Pavillion, and the other is an old Toshiba 440CDT Notebook.)

The modem error message on my new XP system reads as follows:

"Connected phone oline is not compatible iwht this modem. Only analog lines are supported"

After clicking "OK" to close the message box, I got another message which reads:
"Opening Port
Error 680: There was no dial tone"

I first thought the modem error was caused by my Logitech Cordless Max Duo keyboard and Mouse system. But after switching back and configuring to a standard corded-mouse, I got the same error messages.

Here is the rub. I took my system back to my vendor and the modem dialed up on his analog phone line to his and my ISP. Granted he used a corded-mouse as the pointing device. As I have described above, switching to a corded-mouse didn't not work with my analog phone line(s)either.

What else should I try?

This bug that affects the modem only on *some* phone lines, has been corrected with later driver versions.
Modemsite's Premium Access area has them, and you may find them also from Windows Update.