Even so, the OP would be able to get use of all 4GB of RAM and not the 3.25 that LFC said. So if the OP did install 64 Bit, he would get the 4GB but no more. There is a difference between the chipset not allowing more than 4GB and mistaking the chipset to limit you to what Windows 32 Bit does.
the memory address bus is not the same as instruction width
A 64-bit CPU can execute instructions that a 64-bits wide, if a 64-bit OS is used. Then, the CPU runs in 64-bit mode and cannot process 32-bit instructions (hence the WoW 'emulator' to pad 32-bit instructions to 64-bits, so that it can run 32-bit executables)
In the case of Intel systems before socket 1366/1166, the chipset contains the memory controller. Which means that the address bus width depends on the chipset.
If the instruction width is 64-bit, but the memory address width is 32-bit, it can still only address 4GB memory.
Most of Intel's core 2 compatible chipsets have a bigger address bus than 32-bits, enabling them to address more than 4GB when a 64-bit OS is used.
Also, AMD's K8 (Athlon 64) CPU's, with the memory controller integrated, have a 48-bit address bus, which means the memory controller can address a maximum of 2^48 = 281,474,976,710,656 bytes (256 terabytes), even if the OS can make use of a 64-bit memory address (with a limit of 16 exabytes)
If a 32-bit OS is used, it can use a 32-bit memory address width or lower.
If a 64-bit OS is used, it can use a 64-bit memory address width or lower.
Also, the memory address space includes both system memory and video memory.
If you have a 1GB video card, that's 1GB less address space that can be used for system memory.