Do you still see a modem LED when computer is off? On some computers LED doesn't go off, but power is not sufficient for the modem, it is hanging. It stays hanging when you power on computer again. There is a settings in the BIOS to remove power from USB ports when power if off.
If modem LED goes off, there is other possibility. Look at the boot options and remove booting from CD-ROM, or remove USB legacy support.