Hmmm... The problem isn't a power SURGE, but rather a sudden drop in AC line voltage (ex: mini-brownout). A surge would be a sudden spike (voltage transient) going down the line well in excess of the regular ~110V AC.
A surge supressor will do you no good here...
There isn't a whole lot you can realistically do about this. One thing is you could rewire your air conditioner so that it has better line isolation from the power lines that go into your main house. But, normally air conditioners are already wired up on there own seperate circuits though with their own sperate circuit breaker. So, chances are you can't do much in that case.
The only other thing you could do is open up your monitor and install an additional DC capcitor where it is needed. I don't know to much about monitor electronics, but my guess is that they run on DC power. I'm presuming they use transformers and bridge rectifiers to produce the huge 60kVolts used in the tube, and another transformer/bridge rectifier to produce the lower DC voltage for the other components. I could be mistaken, maybe monitors use AC voltage, but I somehow doubt it.
Anyways, you would need to add capacitance somehwere after the bridge recitifer one one or more of the described power circuits.
That way, when the AC voltages drop considerably, the capacitors work as quick discharge batteries and keep the device running at full power until the AC voltage is restored.
You might possibly be able to put a non polarized capacitor in circuit of your AC lines near your monitor, but I'm not entirely certain what that would do. I very much doubt that would do anything though. If the minor inductance of your household wiring allows for a large drop in your AC line voltages, I doubt a puny non polarized high voltage capacitor could do anything to speak of at maintaining proper voltages during a brownout condition.
The only other possible way to remedy the problem would be to somehow decrease the inductance of your household wiring. But assuming you don't have any unceessary loop dee loos around iron in your main household wiring, you really can't decrease the wiring's inductance...
The simple answer is you are screwed. There isn't much you can do about it other than buying something like a UPS device that provides the power to your computer when the AC mains power has dropped too low. But even a UPS device takes time to initialize and start providing power. That small delay may be enough to cause the flicker you described all by itself... Maybe not... Depends on the switch on time of the UPS device...