@Barkingmad :-
Hallo, Will.
Well; you don't have a Pentium 4, and it doesn't have H/T..!
What you DO have there is a Pentium D; an early, pre-"Core" architecture dual-core Pentium. These are two separate physical cores, so actually an improvement over the P4's second "virtual" core.
It uses the 'p4-clockmod' governor because these Pentium D's used the same 'NetBurst' architecture as the Northwood Pentium 4s. The P4s couldn't make use of a governor because they didn't actually possess the necessary Intel 'Speedstep' technology required for the governor to work; this was introduced with the Pentium D's sibling, the Pentium M.
So, yes; you DO have a 64-bit capable CPU. As for which Puppy, given the accompanying chipset - the 945 - my recommendation would be to take a look at Xenialpup64. Others will recommend using the newest Puppy possible; I know bigpup certainly will. Xenialpup's 'parent', Ubuntu 16.04 LTS 'Xenial Xerus' has just gone EOL, but that's of no consequence to us; Xenial64's requirements are lighter than Bionic or Fossa, you've got fairly old tech there, so don't really need the newest kernel to support it, and all the current browsers still run fine with it.....I run it myself, so I can confirm that.
You can of course ignore my ramblings if you so wish, and give the newer 64-bitzers a try. It's your decision at the end of the day.
Mike. 