Modems "accidentally" connected to directly to 240v can "become faulty" and need replacing.
A replacement modem would give you a definitive answer.
I would never condone doing this. Doing this would be naughty and bad and potentially kill you and be fraud and I'm sure I'll trigger 500 angry replies so don't do it.
Of course Geekzoners would never dream of doing such a thing. We are above that.