No no no. See, Windows 7 product keys are edition specific but not architecture specific. That means the home basic key can only be used to activate a home basic install (both 32 bit and 64 bit) but it cant activate any other edition.
Windows 7 disks are generic so they contain all edition images though these may need to be unlocked. But a single pre-manufactured disk wil only contain either 32 bit or 64 bit.
Dude listen, dont get into the technicalities. As I had advised earlier, find a generic Windows 7 disk on the net or from a friend, install the edition that is written on the sticker, then activate with the sticker key.