What is your Video card? What is the VRAM? You must not have enough available(not total), as III only requires 32mb of vram, as I use to play it on a XP Home laptop with a cheap VIA/SIS card w/32mb vram and an 798MHZ AMD Sempron with only 256MB DDR Ram, on a laptop, and on an XP Home desktop w/ VIA/SIS card w/64mb vram and the same RAM and processor as the laptop(except the processor speed was 2.0 GHZ). The reason I mention the available vram and not total, cause just like the RAM, you can have say 1GB vram, but less than that is available because of it being reserved for other applications and programs on the computer.-for example, on my desktop, it says I have 1407MB of VRAM, but only 256MB is Dedicated to games.
Also, try Windows 98 or XP compatibility mode, but it shouldn't be needed unless you have a graphics bug and/or the infamous random mouse freeze issue that occurs on Vista and occasionally(very rare) on Windows 7 and XP SP3. Also, ARE ALL your drivers up to date for your Video card, Sound card, DX, etc.?