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Dos box checks the refresh rate? As far as I know, dosbox just sets a resolution and color depth, and lets the OS determine the refreshrate, and the OS in turn decides if the monitor can handle it. Apps don't need to do that manually, only dos apps do (and no, dosbox is not dos app...).
The same goes for ntvdm, I would think.
dos32a also doesn't have anything to do with the refreshrate. It's a protected mode memory manager.
If Settlers2 makes use of Vesa standards to display graphics, you might try univesa. It's a TSR (terminate and stay resident) program that helps when your videocard is not vesa compliant. But, this is a dos tool, and I don't think it has any use on Windows machines. It may not even start. If you can't find it, send me an e-mail and I'll reply back with the program.
Forgive me for continually doubting you, but I still think there is something different going on here. I'm also still not convinced it's a refreshrate problem, because your monitor says frequency out of range, and still displays garble. When it says that, the frequency in question is also not mentioned as menu title of the OSD menu that appears?
Could you give details about your computer hardware (video card most notably) and software BTW?