So you had win7-32, wanted 64, bought a new license and installed it....so you have an extra win7 license laying around?
Regardless if it's 32-bit or 64-bit, two computers = two licenses. If the first license was OEM that you purchased from somewhere like newegg, you'll probably have to call it in. If it's OEM from Dell/HP, you'll be SOL. If the licenses are retail, you shouldn't get any shit...though you might have to call it in anyway if you activated the old license recently.