Apologies in advance if the first part of this comes off a bit argumentative, but I think there is an important point about physical theory that should be made. This point is also implicit in David Zaslavsky's answer as well.
Rant on effective theories
Actually trying to calculate macroscopic properties like "chemistry" from fundamental theories like QCD and QED, or string theory, etc. seems to me to be missing the point of much of modern physics. In particular, there's enough of a separation of length, energy, and time scales that the "physics" that goes into the boiling point of Nitrogen is almost completely disjoint from the physics of quarks and and the nucleus.
Indeed, if to do any physics we had to start from the very bottom every time, science in a form usable and comprehensible by humans could not exist! One of the deepest ideas of the 20th century is the notion of "effective field theory and renormalization" which to me makes clear why we can treat all the effects coming from high-energy physics as "just" couplings going into our vastly more useful phenomenological theories, i.e. all we get out of particle physics is some numbers such as the mass of various particles, or effective interaction potentials such as the Coulomb interaction, etc. and these numbers are just as useful if you measure them from doing experiments as if you were to calculate them. (And as calculating many of these (with some notable exceptions) involves intractable many-body problems, at this point in time it's actually much more accurate to measure them).
Breakdown of scales
In this particular case of determining boiling points, let me lay out what I think the relevant scales are from the bottom up and perhaps real experts can come by and correct me.
QCD and "below"
First of all, effects from nuclear physics and below are totally negligible, as pointed out by David Zaslavsky already. So we can just treat the nuclei (and electrons) as single particles and take the masses as something given from measurement. If you wanted to calculate these masses, it's my impression that there are pretty good models for the masses of nuclei if you have the masses of protons and neutrons. However, the masses of protons and neutrons have not been (directly) calculated to any reasonable accuracy up until fairly recently, if at all. And these models assume certain values for quark masses, which I think nobody really knows how to calculate at all. In any case, you could certainly dig deeper and deeper with respect to calculating the masses of things, but other effects won't be important for the boiling point of nitrogen.
QED and quantum mechanics
Second, higher corrections from QED and indeed, even quantum effects between molecules will probably be ignorable too, since for Nitrogen at its boiling temperature, the molecules will be far away from quantum coherence (I'm less sure of this, but a quick check by estimating the de Broglie wavelength seems to work out; note that this will not be true for liquid Helium or Hydrogen). What this means is that you can probably get away with treating the Nitrogen molecules as classical (dumbbell-shaped) dipoles with an effective pair interaction coming, as David Zaslavsky pointed out, from a single-molecule quantum ab initio calculation. I'm not sure if current techniques allow for this to be done with any reasonable accuracy, but with 14 electrons, it is a fairly serious problem not too far away from the current frontiers in the field of quantum chemistry.
Classical molecular dynamics
Now we get to scales which are to me, more interesting, and where the physics of boiling finally appears.
As David Zaslavsky and mbq have pointed out, boiling point is a thermodynamic property, thus it is something which only exists for a macroscopic number of molecules. That said, one won't need to attempt a simulation with 10^23 Nitrogen molecules to get a reasonable estimate; one of the triumphs of statistical mechanics is an understanding of how to estimate "finite-size effects"; however, it should be emphasized that this is yet another many-body problem (read as, impossible to solve analytically, requires difficult computer simulation to get right).
So finally, to get the boiling point, you could model Nitrogen molecules as some kind of pair-interacting dipolar gas in a classical molecular dynamics simulation at fixed pressure, say, and tune the temperature up until the molecules in your simulation begin to behave in a gaslike way rather than liquidlike (this "behavior" can be made more precise with the notion of pair correlation functions, for instance). Note a few things here. The greatest error in your estimation will be coming from your ability to put in a bunch of particles here in a controlled fashion in your simulation. This is going to vastly outweigh any error from the steps "further up" other than having a good effective potential. This explains why scientists who actually do molecular dynamics simulation don't spend that much time worrying about QCD and particle physics.
Places to start looking and references
OK, that all written, I've looked around for some references that would be useful on molecular dynamics simulation of liquid nitrogen.
Dominique Levesque and Jean Jacques Weis write in the 1992 book The Monte Carlo Method in Condensed Matter Physics a chapter "Recent progress in the simulation of classical fluids" which goes over the main computational techniques commonly used now. This contains a short section on Nitrogen, as well.
Javier Carrero-Mantilla and Mario Llano-Restrepo, Fluid Phase Equilibria, Volume 208, Issues 1-2, 15 June 2003, Pages 155-169 writes on simulation of liquid Nitrogen and binary mixtures with some other simple liquids. I've attached a figure from the paper which shows the liquid-vapor coexistence curve as a function of density, from which you could read off boiling point if you wanted. The agreement is pretty amazing, and they do use the strategy I outlined above - simulate Nitrogen as a classical fluid with a tuned intermolecular potential; their source for the potential is apparently C.S. Murthy, K. Singer, M.L. Klein and I.R. McDonald, Mol. Phys. 41 (1980), pp. 1387–1399..
I could dig around more for newer references, but if you're really interested, you can use google scholar and some of the search terms like "ab initio", "liquid-vapor coexistence", "Liquid nitrogen", "molecular dynamics" to find more...