After effect is a 32bit application, so it won't be able to get more than 4GB of ram per process. If Windows 7 32 is like Windows Vista 32, AE won't be able to use more than 2Gb per process and more that 2,7gb as a whole because of Windows limitations.
As AE CS3 & CS4 are 32bit application, even in 64bit environnement, they won't be able to use more than 4gb of ram in a single process, but if you enable multiprocessing, each new instances of AE will be able to access to 4gb of ram also, with a max of 16b of ram.
If you have a quad core, and want to use all your processor cores, you will need at least 8gb of ram, because AE needs at least 2gb per core.
So my advice is, drop Win 7 32bit for a Win 7 x64 AE will love you more, and use more of your power.
As Sébastien said, if you can, go 64bit with a decent amount of RAM so you can use multiprocessing. For a quad core, that would ideally make 16GB, but 8GB or any higher value inbetween should be okay as well. The only caveat is, that CS3's MP model was a bit "dumb" and it doesn't allow you to exclude cores, so it wil leitehr always be on on all cores or you just use one core for normal renders. Therefore, once you have sorted out the hardware, perhaps make plans to upgrade the software also at some point...
Hey guys - coming across this thread a while after it started . . . but could someone explain how After Effects CS4 as a 32 bit program will work in my new Windows 7 64 bit system (with 24GB RAM). I do have a Quad Core with hyperthreading. Wasn't clear from previous remarks if people were saying all four cores could be engaged by opening After Effects 4 times and assumedly running smaller projects on each simultaneously? Or if there was some way to get AFX to 'see' more than the 32bit limit of 4GB at a time?
Thanks for any clarifications on this.