To me it sounds like the game is trying to display a higher resolution, or refresh rate, than your screen can handle (depending entirely on what screen you have). I myself have an old CRT scren hooked up to my mini (a PPC one though, but since you say that the game does run, albeit without graphics, I don't think that matters much), and it flickers a lot and shows a load of ghost images when the resolution/refresh rate is too high (such as Warcraft III is set to by default), LCD's and other/newer CRT's may display a blank screen instead (I don't know)... you can get into the video settings in the game by pressing O V when the game has loaded (in that order, not at the same time, and wait a second or so between the keys for the menus to roll up and down), but there's no keyboard shortcut for changing the resolution when you've come that far, sorry.
One solution is to hook up a screen that you know can support a higher resolution then change to the lowest resolution, switch back to the other screen, and lastly raise the resolution step by step and clicking OK every time it looks good (the game will switch back to the resolution you had before if you don't click OK in 10 seconds or so).
The other I can think of (but doesn't work on Intel machines, since they don't have Classic), is to manually edit the file "Warcraft III Preferences" with the old program "Resedit" (or if a similar program exists for OS X, in which case it should be possible on Intel macs as well)... I can even guess what resource should be what value, they have fairly descriptive names (except they're in the form of Windows registry paths, YUCK), and seem to be hexadecimal values.
glad you got it sorted