The Mac to VGA adapter doesn't tell the monitor anything. It tells the Mac what kind of monitor is attached, and then the Mac adjusts and outputs that resolution. From the resolutions you listed for the LCD and the two modes for the Adapter, I would bet that the adapter is causing your Mac to output resolutions which your LCD cannot display.

In other words, you're on the right track, try a different adapter. I find the ones that look like this:



very usable. I used to sell them for $4.50 shipped, but I ran out a year or two ago.

I think I saved about 150 of them from the landfill though...

Huh. Someone sells them on Amazon:

http://www.amazon.com/Sony-UniMacFly-Unimacfly/dp/B000MKN29O