This probably won't help unless you're an electronics techie, but just for clarification, this is probably what's happening:
(I'm assuming that you're using a CRT monitor as those symptoms are unlikely to happen with an LCD). CRTs are sensitive to electromagnetic fields, including the earth's magnetic field. When power is off, stray magnetic fields may leave a semi-permanent effect, causing undesireable effects on the colour or picture geometry.
When you first switch on the monitor, a powerful alternating magnetic field is generated in a coil surrounding the picture tube for a brief moment to erase the effects of any stray magnetic field. An effect of this erasing field is to violently shake the visible display.
Normally, power to the coil is automatically reduced after a second or so, and by the time the tube has warmed up and the POST screen appears, the effect has disappeared. The electronic circuit that regulates the strength of current flowing into the coil may be defective, causing the electromagnetic field to stay high longer than it should.
If this is the case, it is not a difficult repair job for a competent technician.
A second possibility is that the main filter capacitor in the monitor's power supply has grown weak and cannot do the job properly until it has warmed up. Here the solution is to replace the capacitor. Another easy job for someone who knows what he's doing.
Theoretically, the second possibility can also happen with an LCD monitor, though I haven't come across such a case so far.
