Is the power drop continuous or intermittent? If it's intermittent then you might want to check the connectors on the AC Adaptor. The wall plug, the box itself, and the plug going into the back of the laptop, and also check the wires for any fraying/holes in the insulation and such.
Also try reseating the battery. My laptop always flickers slightly in brightness when switching power sources, and this sounds like what your laptop is doing. Also, keep in mind, most laptops 'store' different brightness settings for AC power and Battery operation. Try setting the brightnesses differently so you can tell what it's running off of at any given time, since the taskbar entry doesn't update as often as it should.