It's there when you open the wine and pour it into your glass or it's in the cases? If the wines are corked, you'll tell in the glass. If it's just the cases, take the wine out and put it in something else.
Maybe your glasses are musty from sitting in the cabinet? Not uncommon. And some wine has naturally funky aromas that are very different from corked wine. What are the wines?
Storage problems won't make the wine corked either. Usually the wine just ends up overheated and you can't necessarily tell from looking at the bottle. In fact, you often can't tell period - wine can be surprisingly resiliant.
Both cheap and expensive wines can be corked, so that won't make much difference. There are a few really expensive Nero d'Avolas, but most are pretty inexpensive and to me, pretty good too. So you may have some decent stuff there.
In any event, it's really unlikely that every single bottle in two cases of such different wines are going to be corked unless the importer just collected all the returns from his customers and gave them to your dad. And that would be so hilarious that you'd have to give him much respect.