If connections are OK then check for bad wires by wiggling short sections of the cords while monitor is on, see if anything happens.

If you don't get any reactions from those tests...
Is it a skinny LCD flat screen or a big heavy CRT flat screen monitor?

If not heavy can you move it around or shake it to see if that makes it go on/off??

It would be one way to maybe find out if it is an internal problem or external.
internal not as easy to fix, a wire or connector can be replaced.