Modem keeps line busy, phone port is dead

As far as I can tell, the linuxant driver is working correctly. I can
connect to the tty with a terminal program and I get responses to AT
commands.

However, the modem keeps the phone line always busy. The modem also
has a "phone" port intended to let an external phone be used when the
modem is inactive; a phone plugged there and an unplugged phone behave
in the same way.

Is this something I can fix, or is it a hardware problem?