How do holes conduct current?
It is not true that the valence band cannot contribute to conduction. That's just what happens in P-type semiconductors. The doping alters the band structure of the semiconductor so that there are "missing" electrons (holes) in the valence band. This allows other electrons to "move" from an atom to a nearby one without jumping into the conduction band: they fill a hole "near to them", leaving a hole "behind them". This mechanism is modeled by virtual charges (the holes) moving in the opposite direction. All this happens in the valence band, and this is (intuitively) the reason why the mobility of holes is less than that of electrons. Actual conduction is always due to moving electrons, but when conduction happens in the valence band all is more "difficult" (the energy of the moving electrons filling hole after hole is less than the energy they would have if they were in the conduction band). Bear in mind that this is only a qualitative explanation. This is something in the realm of quantum mechanics and solid-state physics, and the equations involved are rather nasty.

BTW, what you mention by "holes attract electrons from conduction band" is called recombination. In a P-type semiconductor there are very few electrons in conduction band, and they are due to thermal generation (the higher the temperature the higher the probability that a free electron-hole pair will be generated). So it is true that very few electrons in conduction band will contribute to current in P-type semiconductor (they are the thermally-generated minority carriers). But the bulk of the current is supported by holes "moving" in valence band, as I explained above.