With regards to lemon law, what if the product was broken due to negligence and mishandling instead?

Firstly, it depends on the nature of the product and whether it is covered by lemon law, or the Consumer Protection Fair Trading Act.

Next, we have to establish whether there exists any form of unfair practice, e.g. making a false claim that the item is of satisfactory condition when it is otherwise.

Thereafter, we will have to determine whether the item was transacted at a satisfactory condition at the point of sale. Since item was broken due to negligence, there is no case. =)

That would be fraud! I guess each company has different policies with this; for very proftiable business (eg kids toys), likely they let slide and just refund. For marginal businesses (computer parts) would look harder into contesting, particularly for high value items.

Also depends on industry type - in financial services, there may be regulatory limitations on how complaints are handled.