I take it since you only have the 32-bit version, it's an OEM version so it even worse, if you try it on a different computer, it would state that your hardware has changed and invalidate the key for that machine.
This is why I no longer buy OEM. Too many hassles when you do major upgrades and the licenses are not transferable between computers. With the retail versions, the key is transferable to a different machine. Of course, it means it won't work on the previous machine anymore unless you transfer the license back to that machine and invalidate it on the other machine.