Thank you Michael,
I earlier tried that, but had negative results. Did again and more promising this time. I think it is time to buy a new modem.
I couldn't find anything in /dev/directory, but did get this:
[root@desktop dev]# dmesg | grep tty
console [tty0] enabled
cdc_acm 3-2:2.0: ttyACM0: USB ACM device
The modem is now working, so thanks again. Funny thing happened, however.
I unplugged the modem and plugged it into a different USB. Bunch of text covered the screen on the physical machine, and then Linux rebooted without asking me. Is this normal? Sounds like something Windows would do