Unless (by a chance) Sony has preloaded 32-bit drivers onto original Windows installation, you cannot use same drivers.
The drivers contain files with .INF extension, which describes what the drivers is for, and how to isntall it. Look at your disk after restore, whether you can find any of these files outside Windows folder. They might be also provided on separate (hidden) partition. And while you are here, make sure you have made the recovery media as well.
There is another option: Install your 32-bit Windows inside virtual machine. I am not sure Microsoft' VirtualPC will work on Home Basic edition, but e.g. Oracle' Virtual box should work.