The last Intel chip for PC's that did not have 64 bit support was the Pentium 4 which finished it's run in 2008. So yes, you are talking at least a 10 year old computer. Note: Some Pentium 4's did support 64 bit, that's just the last chip Intel made that didn't. For embedded computing 32 bit chips still exist, you will not find those in PC's.

That isn't to say people weren't running 32 bit OS on 64 bit platforms, there is no reason you couldn't still do that. Except of course it would be extremely stupi... er "inefficient" to do so.