It is very common for a repetitive "clicking" noise to be "Power Related". This goes for Computers, Monitors, even Vehicles.
Either the Power Cord from your Monitor to the outlet may be close to shorting out, or something internally (in your monitor) may be loose/frayed.
If you trust yourself with "Hardware" related components, I'd recommend peeking inside of your monitor tracing your power cord TO it's source on the board inside of your monitor. Check for any loose cables or anything that looks possibly "burned" or torched.
(Insurance : If your monitor is seriously as bad as it seems, any damage that may occur when "popping the hood" so to speak, can't be that much more damaging.)
Report back with changes, and possibly a couple pictures.