Another post on this board (mentioning hardware acceleration) inspired me to do this: I had never been able to see the video effects with hardware acceleration in MM7. After fiddling a bit more with my video card, I played a hunch and decided to "force" MM7 to use hardware acceleration, even if it "thought" that it couldn't. I did this with the registry editor. It worked! I now have the colored lights, and fog effects and such... And better yet, I have an excuse to play the game again!

Here's the exact method, in case you want to try this too. It's a long shot. And if you're the sort of user who can't fix your computer after you break it, don't use regedit at all.

Run "regedit". (From the Start menu, choose "Run" and type "regedit".)
Navigate the tree to "HKEY_LOCAL_MACHINE/Software/New World Computing/Might and Magic VII"
Change the "Use D3D" value from 0 to 1. (Right click on "Use D3D" and select "Modify".)

Relevant bits of info for my system are:
Windows '98 (kind of bastardized with random extra components)
Video card: ATI Xpert 2000 Pro (set to AGP 2x)
DirectX 9.0