I believe dmckee is right when it comes to the physics of board breaking. I might not have his physics credentials, but I've still studied a bit of it myself and would have made the same argument. Whatever technique you are using to break that board, if the strain is greater than the local resistance of the board, it will break. This is influenced by the nature of the material as well as it's geometry, and that's pretty much it. No matter if someone has strong punching power or not, as long as he has at least the minimum power required to break the board, he will break it.
In the next part of my answer, I will try to stick to "physics 101", and try to outline where it is insufficient in answering the question accurately. I invite dmckee and other more versed than I am in physics to correct me if I make any mistakes. My only wish is that the spirit of this answer (its reliance on "physics 101" and the outline of it's shortcomings) remains untouched.
Concerning your update... In my opinion, no matter what kind of biometrics you have access to, there is no way to measure someone's punching/board breaking power without actually having them punch/break boards.
This is because the use of momentum in martial arts is way more complex than simply measuring your weight and speed and multiplying them together. Sure, that's the gist of it, but what portion of your total weight do you actually put behind your punch? It can depend on a lot of different factors, such as the quality of your stance or the efficiency of your weight transfer.
As an example, let's say I weigh twice as much as you do. According to you, I'd automatically have double the punching power. This interpretation is somewhat limited. What if I only punched using my arms, without regards to my stance or without shifting weight to my punch? If you had a better technique, you could easily achieve superior punching power. Momentum can indeed help you determine the punching power of an individual but, sadly, it's just about impossible to measure accurately, as there are too many factors to consider.
And even then, as dmckee said, that's not counting on the internal forces that you are applying to your body while punching. Different individuals will have different tolerances allowing for more or less powerful punches. What good is punching at your maximum power if your hand/elbow/joint/etc. breaks just as much as the board? Psychological limitations will also play a part here. Even given superior potential, someone afraid to injure himself (you are attempting to hit wooden boards, after all) will be at a disadvantage compared someone confident in his ability.
And about kinetic energy? Assuming the perfect punch, where you are able to transfer 100% of your energy to your target, kinetic energy becomes a measure of your maximum potential damage on that specific strike. But, like momentum, what mass are you using in your calculations anyways? Only that of your fist? Of your whole body? And once again, the amount of kinetic energy you will be able to transfer as a deformation to your target depends on the target's nature, it's geometry and your own capacity to strike accurately on a location that will maximize the damage. And, not surprisingly, the momentum of your strike is a direct measure of how difficult stopping your punch will be, and thus influences greatly the amount of kinetic energy you will transfer to your target.
Wether you want it or not, both kinetic energy and momentum will matter in some way. Unfortunately, they are pretty much impossible to measure without actually breaking progressively harder boards, as there are too many different factors to consider, some of which even the best doctors probably wouldn't think about.
I hope this shed some light on the situation for some of you, and I do hope I have not made a big fool of myself...