Sounds to me like it is the cable that connects from the PC to the Monitor. Often, the individual wires inside the cable will break. When you "wiggle" the cable, you help make and break the connections inside the cable causing the picture to change.....
Does the cable unplug from the monitor? If so, it is a simple process to swap out the cables.
If the cable doesn't disconnect from the monitor than the process becomes a little more involved, and you might consider taking it to a computer store. There they can probably replace the cable for you....
WARNING
If this is a CRT type monitor, there can be VERY HIGH VOLTAGES PRESENT: Do not attempt to fix yourself unless you are experienced with electricity
Good luck, and let us know how it works out....
Junior
Planes and computers.....
Both are great untill they crash.