Yours is a classic problem created by transient from AC
mains. Common mode transient sought earth ground. Incoming
on AC wire that makes direct connection (through motherboard)
to modem. Outgoing to earth ground via phone line. Since the
surge was so minimal, a PNP transistor that drives off hook
relay is permanently shorted. To get phone line free, remove
phone line from modem OR remove power to computer. Second
condition must be true if this is PNP transistor problem.
Modem can be repaired by soldering a new PNP transistor
between modem controller IC and that off-hook relay circuit.

Your failure suggests no 'whole house' surge protector was
installed on the most common source of lightning damage - AC
electric. Lightning found earth ground via your modem
regardless of whether you had computer powered. Even worse, a
plug-in and adjacent surge protector makes this type of damage
more probable.

Chief Thracian wrote:
As of two weeks ago, I can no longer Internet-connect
the usual way, via my Supra Express 56k modem. (My OS
is Windoze98.) Here's the problem:

I need to unplug and replug the telephone line going to
the modem, to restore the dial tone. If not, the phone
line remains open, so I can't receive or send phone
calls. It's as if the modem lost its ability to hang
up. (Problem remains even when my computer is shut
down...so I know it's not OS--or even
computer--related.)

Now, when I don't need to get on the 'net, I unplug the
phone line from the modem, and plug it into the back of
my answering machine... which then allows me to receive
and make regular phone calls.

Is this a burnt-out modem chip? Or can I possibly
restore my modem to its former excellent condition?
Where do I start? I have yet to find the appropriate
help file. If you know of one, please direct me to it.
Otherwise, I'd much appreciate someone guiding me
through possible maneuvers to correct the error.

TIA.