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#11
64 bit Windows and programs isn't the problem, it is as you say the "old" motherboard/chipset. Also it isn't the motherboard that determines 64 bit, but the CPU.
Even if he installs 64 bit Windows the available ram won't change. The reason being is that the Intel G31 chipset only supports up to 4 GB,
ARK | Intel® G31 Express Chipset (Intel® 82G31 Graphics and Memory Controller)
which will result in this,
The system memory that is reported in the System Information dialog box in Windows Vista is less than you expect if 4 GB of RAM is installed