Well I once had a P4 HT 3.06GHz in an old HP dx2200 of mine and I ran 64-bit Windows on it just fine. Probably best to stick to 32-bit though, you likely have less than 4GB of RAM making 64-bit not worthwhile.
Not all P4 HTs are 64-bit compatible either. Download CPU-Z and gimme a screenshot and I'll look it up for you.