It is a software issue with the driver of Intel GM965 Integrated Graphics. You should disable the Refresh Rate switch at plug/unplug in the driver's control panel. It is used as a power saving feature to switch from 60Hz to 50Hz at unplug, but it conflicts with the driver's other power saving features and something from Lenovo.
I don't have a X300 at hand so I cannot give out any instruction for you. But I think right click on desktop and there should be a menu looks like "Display Properties..." will bring you the interface that contains the said options.
@nothappy1 No I think screen dimming is because on AC/Battery uses different setting for brightness. You can adjust the brightness with FN+PgDn/PgUp. The refresh rate setting may be in the Power Saving tab of the Display Properties interface.