Did the tech who came out check your signal levels for your internet service while he was there, or just swap the modem out? I have no clue if a monitor could have that effect on a modem, I would guess the modem wouldn't turn on at all if it was zapped by the monitor.
Because the modem is still alive, but cannot get a signal, it sounds like you may have a signal issue on your cable line. Did you try moving the monitor away from the modem? Do you have any devices that are emitting a lot of RF near the modem, such as wireless router, cordless phone, microwave, etc? If so, try moving the modem away from that stuff, and the computer itself. Worst case, you're looking at another tech coming out to take a look. Make sure he checks your signals!
good luck!
z