At the moment, the English translation for this is "I don't like sad books at all", and not "the sad books". But I noticed that the Turkish is "üzücü kitapları" and not "üzücü kitaplar". What is the '-ı' referring to here? Is it due to being a definite accusative, or is it because of the "üzücü"?
Sainio is correct.
As an aside, for this particular sentence, even if the "nasıl" were elsewhere, and the object were immediately before the verb, you would still have an "-ı" there. The reason for that is, plural objects almost always have to be in the accusative case.
You could simply use singular, too, by the way: "Hiç üzücü kitap sevmem," or "Üzücü kitap sevmem hiç." (Notice how I moved the "hiç" elsewhere so as not to have to use the 'kitap' in accusative.) This means exactly the same thing as "Üzücü kitapları hiç sevmem."
I still don't understand why üzücü kitapları is in the accusative here. It is clearly an indefinite object. Someone in the thread suggests that it is because the object does not immediately precede the verb, but I cannot find anywhere that says there is a rule that indefinite objects that do not immediately precede verbs get the accusative.
It is true. If your object isn't next to the verb, it has to be in the accusative. Though hiç is such a short word that leaving out the accusative would still be okay. The problem here is that, leaving the object in the nominative form and also pluralizing it sounds bad in TR. Indefinite objects should better be singular. So your options are:
Üzücü kitap sevmem. Üzücü kitapları sevmem. But not "üzücü kitaplar sevmem". That sounds unidiomatic even if it's next to the verb.