The IGM would have remained predominantly neutral until `subgalaxies', with total (dark matter) masses above 108 M and virial velocities 20 km/s, had generated enough photoionizing flux from O-B stars, or perhaps accreting black holes (see Loeb (1999) and references cited therein).
How many of these `subgalaxies' formed, and how bright each one would be, depends on another big uncertainty: the IMF and formation efficiency for the Population III objects.
The gravitational aspects of clustering can all be modeled convincingly by computer simulations. So also, now, can the dynamics of the baryonic (gaseous) component - including shocks and radiative cooling. The huge dynamic range of the star-formation process cannot be tracked computationally up to the densities at which individual stars condense out. But the nature of the simulation changes as soon as the first stars (or other compact objects) form. The first stars (or other compact objects) exert crucial feedback - the remaining gas is heated by ionizing radiation, and perhaps also by an injection of kinetic energy via winds and even supernova explosions - which is even harder to model, being sensitive to the IMF, and to further uncertain physics.
Three major uncertainties are:
(i) What is the IMF of the first stellar population? The high-mass stars are the ones that provide efficient (and relatively prompt) feedback. It plainly makes a big difference whether these are the dominant type of stars, or whether the initial IMF rises steeply towards low masses (or is bimodal), so that very many faint stars form before there is a significant feedback. The Population III objects form in an unmagnetised medium of pure H and He, bathed in background radiation that may be hotter than 50 K when the action starts (at redshift z the ambient temperature is of course 2.7(1 + z) K). Would these conditions favour a flatter or a steeper IMF than we observed today? This is completely unclear: the density may become so high that fragmentation proceeds to very low masses (despite the higher temperature and absence of coolants other than molecular hydrogen); on the other hand, massive stars may be more favoured than at the present epoch. Indeed, fragmentation could even be so completely inhibited that the first things to form are supermassive holes.
(ii) Quite apart from the uncertainty in the IMF, it is also unclear what fraction of the baryons that fall into a clump would actually be incorporated into stars before being re-ejected. The retained fraction would almost certainly be an increasing function of virial velocity: gas more readily escapes from shallow potential wells.
(iii) The influence of the Population III objects depends on how much of their radiation escapes into the IGM. Much of the Lyman continuum emitted within a `subgalaxy' could, for instance, be absorbed within it. The total number of massive stars or accreting holes needed to build up the UV background shortward of the Lyman limit and ionize the IGM, and the concomitant contamination by heavy elements, would then be greater.
All these three uncertainties would, for a given fluctuation spectrum, affect the redshift at which molecules were destroyed, and at which full ionization occurred. Perhaps I'm being pessimistic, but I doubt that either observations or theoretical progress will have eliminated these uncertainties about the `dark age' even by the time NGST flies.