Lightning seeks earth ground. It found a path to earth
through modem's off-hook relay circuit. Therefore your old
modem acted like it was a phone always left off hook.
Lightning seeks earth ground. To damage electronics,
lightning must find both an incoming and outgoing path to
earth. The outgoing path is easy. Phone line is a direct
connection to earth ground through a 'whole house' surge
protector provided free by your telco. However for effective
protection, all incoming utility lines must be properly
protected.
Your damage is classic. Incoming surge was from electric
lines - highest wires on pole that are most often struck.
Since your AC electric had no 'whole house' protector, then
the surge enters your building seeking earth ground. Incoming
on AC electric. Outgoing on phone line. After that complete
circuit was created, only then was something damaged. Classic
damage in your case: off hook relay.
New modem will solve the short term problem. But your long
term problem is that some utilities enter the building without
a 'whole house' protector. Protector that shunts (connects,
diverts) lightning to earth BEFORE it can enter the building.
Plug-in protectors are quite useless as others have noted.
They don't make the essential connection to earth ground -
what lightning seeks. If lightning is permitted inside a
building, then it will find many destructive paths to earth.
Today, you got lucky - only a modem. Next time, how much
more?
Earth a surge before it can enter the building. AC electric
is the most common source of destructive surges. 'Whole
house' protector connected to earth ground is required for
your AC electric - the long term solution. Today a modem.
Only $25+. Tomorrow ... what else?