Unless Oracle has made a drastic change in the last few months VirtualBox
runs very nicely on 32 bit operating systems - at least it always has for
me. Make sure you downloaded the correct version as they have both.

Are you sure you have a 64 bit CPU? One can install a 32 bit O/S on a 64 bit
machine (and I have), but not vice versa. However, a 64 bit O/S probably
requires a 64 bit version of VirtualBox.

Lack of drivers? Very unlikely.

Comments? Corrections?