What's the simplest way to generate a VGA signal for a totally white screen? Preferably with an AVR MCU
Tie the R,G and B lines of a VGA socket to 0.7V (you can use the voltage drop of diodes for this).

Then connect the VSYNC and HSYNC to output lines of a microcontroller.

These two outputs need to be pulsed at the right speed to fake a VGA signal - they are standard TTL-esque signals.

I'll let you do some reading up of the VGA spec to find the right timings for these signals*

*I am out of time but I will add some more information later when I have time about the VGA spec