Monitor - Signal cutting out

My monitor is forever 'cutting' out on me. The screen just goes blank 'for
no apparent reason'. I took it to a friend's and tried it on his PC.....same
result! I can hear a relay (or something) near the monitor's switch clicking
when the picture comes and goes. Also, if I loosen the connection where the
monitor plugs into the PC's video output and wiggle it, the same thing
happens, so does this suggest it's problem with the plug? Or the socket? Or
both? How can I find out what the 'real' cause of this problem is? The video
(chip) is built into the motherboard, not a seperate card. The soldered side
of the socket (inside the PC) 'looks' okay, (where it is sodered onto the
motherboard) but I'm not an expert, so maybe it could be there's something
wrong here? Is there a way to clean the plug's pins and the socket's holes?
What can I use for this job? It's driving me nuts! It 'can' run okay for
hours...'sometimes! Mostly though, it's very erratic and unpredictable. Oh
yes....'when the picture dissappears, the monitor pops up a message to say
that there is no signal input so check all connections.
Any assistance or advice very much appreciated.
Thanks!
C.C.