What happens when you install > 4GB of RAM in a computer with a 32-Bit OS?

If you have a a processor with the Physical Address Extension (which you probably do) and the correct OS (e.g. not a consumer version of Windows, it uses PAE but is capped at 4GB) then the memory can be mapped and used normally. Otherwise the memory will simply not be addressed, the OS will tell that you that you have however many chips of however big they are but they just won't be added to the amount of memory you can access.