Lucretia: your monitor shouldn't make a difference as to whether a game runs or not -- that would be your video card. Anything that can run on a CRT will run on an LCD with the same video card.
Of course, maybe not at the optimal resolution.
For me, I couldn't run Divine Divinity at 1280x1024 because the game would crash to desktop every time I brought up the automap or journal. Beyond Divinity officially supports 1280x960, though, which is fine. Haven't tried tweaking it to get the extra height.
These limitations are pretty much inherent with games that use bitmapped graphics -- they're always more or less resolution-dependent. Hope that Larian moves to full 3D in the next round -- avoids all these problems.
