I played WarCraft III on my Presario with its 8MB TNT2 graphics card with no problems (other than the fact that it had an intolerably low framerate unless it was on the lowest resolution). There are a few possibilities for you:
1. Your drivers are outdated. Half-Life kicked my compy in the nads and made it reboot just like yours until I found and downloaded a newer driver.
2. The graphics mode you chose isn't the most compatible. Does it do the same thing if you switch WC3 to OpenGL, Direct3D, or software rendering (or does it have all three of those options, or am I thinking of Half-Life?)
3. It may be a particular piece of rendering work that screws it up that only appears in higher detail levels. When you say detail levels, are you talking about resolution, color depth, the other options (i.e., unit shadows, etc), or all of the above? If it's the other options, you might be able to find the one that messes up.
4. Your card is simply not very compatible with the way WC3 renders. It happens. I mean, my other comp is an eMachines with a 32MB graphics card, but it can't run Unreal Tournament at anything higher than 512x384 without getting really slow; but it runs Half-Life smooth as silk at 800x600, and with only minor slowdown at 1024x768. That may be the case with your computer and WC3.
Hope somewhere in that mess was something helpful! :cyclopes: