Recently my hard drive was corrupted on my laptop with 32-bit Windows 7 pre-installed. I heard you can re-register the serial keys to work with a new computer, erasing it on the older one, however I wish to upgrade to 64-bit Windows 7 in order to accommodate for more RAM expansions (aiming either for 8 GB or 16 GB). Is there any way I could do this without buying another OS?
There are two important points:
1) Microsoft sells window keys which you can use to install either a 32bit windows or a 64 bit windows, using the same key.
2) OEM vendors (likely what you had pre-installed) come with keys which might only be useful for that specific version.
Without knowing what you had pre-installed there is no way we can guarantee that it will work. However if you already have a broken installation then I recommend making a backup of all data which you want to keep, getting a 64bit windows install disk (e.g. download the iso from digital river), and just trying it.