Under the Sale of Goods act, your contract of sale is with the vendor, not the manufacturer (if they are not the same person/company as the vendor). This means that it is the duty of the retailer to honour any warranty, regardless of whether or not they need to chase their supplier of any goods a purchaser returns as a result of defect. The act (which has been updated [in some form that I can't remember] since 1979) requires that goods must be free from defect (fair wear and tear excluded in the case of a return), be of merchantable quality and be fit for their intended purpose at the time of purchase and for (at least) the first year since purchase. This minimum of the first year covered by warranty is a matter of law, not some nicety on the part of the vendor/manufacturer. In addition, the act states that goods must not be defective as part of manufacture and/or design and that claims on this aspect of the warranty are open forever.
In a dispute/claim on warranty: During the first 6 months, the onus is on the vendor to prove that goods supplied are up to standard, in the second 6 months, the onus moves to the purchaser to prove that they are not. In the case of the crashing laptop, it is demonstrable that the goods are not up to standard as they fail to perform their intended function (viewing pictures). The shifting of the blame to Windows is wrong as presumably the laptop was supplied with Windows and therefore constitutes a component of the goods. The same applies to any additions/modifications made by Asus to the Windows installation. If Windows is at fault (although you have identified an asus dll file as the culprit) then given the performance of the goods, one could argue that they are not of merchantable quality and that they are defective as a result of design/manufacture (and I'd like to be in the public gallery for that day in court).
On the EEEPC's battery charger issue, are you able to test (by multimeter, say) that the charger is dead? If so, I'm sure that it is reasonable to expect a replacement component, rather than whole system, particularly as in this case the components of the system are easily separable. After all, if one bought a new car and the windscreen wiper broke a week later, demanding a whole new car to fix the wiper would seem unreasonable.
If you get no joy on the EEEPC, can you swap out your HD for a blank/other one and send the whole system off? It's not what you should have to do, but it may be the path of least resistance.