Formation of Bands in Semi-Conductors
doesn't explain why electrons in the conduction band are able to conduct electricity while electrons in the valence band can't


Electrons in the valence band can conduct electricity, as long as the valence band is not completely filled. This occurs in semiconductors, when you thermally promote electrons from the valence to the conduction band, you are leaving behind some holes in the valence band. The electrons in the valence band can then conduct electricity as well by "jumping" through the holes. The conductivity of semiconductors arises therefore not only from electrons in the conduction band, but also holes in the valence band.

The origin of conductivity lies in a partially-filled band, and it doesn't matter which band it is. For a more rigorous treatment google for "free electron model". The idea is that each crystal orbital (i.e. MO of the crystal) has an associated value of electron momentum. For each orbital with a positive electron momentum, there is an orbital with an equal but negative momentum. When the band is fully filled, all of the crystal orbitals are filled, and there is no net electron momentum because the positives and negatives cancel out exactly. When the band is incompletely filled, the application of a potential difference in a certain direction across the metal causes the electrons to preferentially populate orbitals with positive momentum in that direction. This leads to a net positive electron momentum in that direction, meaning that electrons "flow".


  The s and p orbitals of the metals combine together to form MOs. [...]


Yes. Bands are simply a collection of crystal orbitals that have such small energy gaps between them such that they are almost continuous. I don't see how the Pauli exclusion principle comes into play except for when you are discussing the population of the orbitals (obviously any one orbital can have a maximum of two electrons). The two ways that I know of to obtain the bands (nearly free electron model, and the LCAO/tight-binding approach) both do not invoke the PEP. However I will add a disclaimer that physicists approach solid state chemistry from a very different direction and there could very well be some explanation that I do not know of.

However, yes, the electrons populate orbitals that are "delocalised" across the entire solid and this is the origin of the "sea of delocalised electrons" description of metals.


  'it is only when these bands become filled with 2p electrons that the elements lose their metallic character'


I honestly don't see how that is relevant or even correct at all. Let's use the example of sodium versus chlorine. The band structure of Na metal is vastly different from that of chlorine since the molecular structures are different to begin with. Sodium is a metal and chlorine is a molecular gas, you wouldn't use a band structure to describe chlorine. You cannot just take a diagram for $\ce{Na}$ and say that it applies to $\ce{Cl2}$ and try to make statements such as "filling of the 3p bands leads to decrease in metallic character" because those bands don't even exist in chlorine. Band structures are just large MO diagrams, it is almost like trying to compare the physical properties of sodium and chlorine using MO diagrams for $\ce{Na2}$ and $\ce{Cl2}$, which is plain absurd.

However, if chlorine were to adopt a structure that has close-packed atoms like in sodium, then you would be right that it would still be metallic due to the partially-filled 3p bands.

If you want to read further I would recommend finding a solid state chemistry textbook, all of them would cover basic band theory. In particular I find this book by Moore and Smart clear and accessible.