The graphics card only contributes to the workspace views, ie whether you can see transparency, textures etc on the screen, it has no bearing on the render. My primary machine is a 1.3GHz Sempron processor (just the single core) so I can sympathize, but I have 1.5GB ram. I have a second machine used primarily for straight-to-avi renders which is a Pentium 4 with 2GB ram and a pair of processors, about the same speed with Anim8or but considerably quicker for Carrara renders as it can make use of multi-threading.
With approx 0.5GB RAM you will definitely run into problems, but it isn't poly counts and subdivision that is the real memory-muncher (particularly subdivision which applies mathematical formulae to the underlying basic wireframe, unless you convert the subdivision object into a wireframe of course), the bigger issue is textures. A basic texture applied to the ambient or diffuse fields, or even bump- and trans-maps, can easily be a couple of MB to get some reasonable level of detail, and only a very complex un-textured wireframe would approach that sort of size. Whatever machine you end up using, make sure it has enough RAM to NEVER need to use virtual memory, VM is much, much slower than RAM. Memory chips are pretty cheap now, best advice (if school computer doesn't work out) is to shove more into your 2.04GHz machine.