Thanks for the detailed explanation
I have been thinking of least expensive possible ways to solve this.
How about connecting my laptop to a docking station and then connecting the vga output to the docking station. Can it possibly have any effect?
Having said that, the power brick is not the only part of this setup that uses switch-mode power supplies. Inside your laptop, there will be separate ones for each of the 12, 5 and 3.3 Volt rails, and one for the CPU core voltage. In addition to these, there will be one or more directly related to the charging of the Batteries, which might be the source of your problem, too. Then there's the switch-mode power supplies within the Monitor, etc.
Hmmm... but if it was any of the other components inside the laptop, then disconnecting the power brick should not have had any effect on the display, while currently as i have previously said, disconnecting the laptop from the power supply makes the display run fine.