A 32-bit OS can actually only use up to 3.25GB of memory (with a 32-bit CPU). If you use your motherboard's integrated video controller, it will likely use your main memory as well for video memory. The others are correct, Win 7 32-bit can use up to 4GB of memory (keeping in mind the use of memory by an integrated video controller).
There is no relationship between the main memory (on the motherboard) and a discrete video card in determining how much main memory the system can use. These are separate from a management standpoint.